메뉴 건너뛰기




Volumn 27, Issue 3, 2010, Pages 323-345

Very singular diffusion equations: Second and fourth order problems

Author keywords

Crystalline flow; Fourth order model; Image analysis; Jump discontinuity; Singular diffusion; Total variation flow

Indexed keywords

CRYSTALLINE FLOW; FOURTH ORDER; JUMP DISCONTINUITY; SINGULAR DIFFUSION; TOTAL VARIATION FLOW;

EID: 79952003125     PISSN: 09167005     EISSN: 1868937X     Source Type: Journal    
DOI: 10.1007/s13160-010-0020-y     Document Type: Article
Times cited : (73)

References (103)
  • 1
    • 0002019195 scopus 로고
    • Uniqueness theorems for surfaces in the large i
    • A.D. Alexandrov 1956 Uniqueness theorems for surfaces in the large I Vestnik Leningrad Univ. 11 5 17
    • (1956) Vestnik Leningrad Univ. , vol.11 , pp. 5-17
    • Alexandrov, A.D.1
  • 2
    • 0027559276 scopus 로고
    • Curvature-driven flows: A variational approach
    • 0783.35002 10.1137/0331020 1205983
    • F. Almgren J.R. Taylor L. Wang 1993 Curvature-driven flows: a variational approach SIAM J. Control Optim. 31 387 438 0783.35002 10.1137/0331020 1205983
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 387-438
    • Almgren, F.1    Taylor, J.R.2    Wang, L.3
  • 3
    • 0000967635 scopus 로고    scopus 로고
    • The dirichlet problem for the total variation flow
    • DOI 10.1006/jfan.2000.3698, PII S002212360093698X
    • F. Andreu-Vaillo C. Ballester V. Caselles J.M. Mazón 2001 The Dirichlet problem for the total variation flow J. Funct. Anal. 180 347 403 10.1006/jfan.2000.3698 1814993 (Pubitemid 33591686)
    • (2001) Journal of Functional Analysis , vol.180 , Issue.2 , pp. 347-403
    • Andreu, F.1    Ballester, C.2    Caselles, V.3    Mazon, J.M.4
  • 5
    • 33847303953 scopus 로고
    • Multiphase thermomechanics with interfacial structure. Part 2: Evolution of an isothermal interface
    • 0723.73017 10.1007/BF01041068 1013461
    • S.B. Angenent M.E. Gurtin 1989 Multiphase thermomechanics with interfacial structure. Part 2: evolution of an isothermal interface Arch. Ration. Mech. Anal. 108 323 391 0723.73017 10.1007/BF01041068 1013461
    • (1989) Arch. Ration. Mech. Anal. , vol.108 , pp. 323-391
    • Angenent, S.B.1    Gurtin, M.E.2
  • 6
    • 84975945844 scopus 로고
    • Application des méthodes de convexité et monotone à létude de certaines équations quasi linéaires
    • Attouch, H., Damlamian, A.: Application des méthodes de convexité et monotone à létude de certaines équations quasi linéaires, Proc. Roy. Soc. Edinburgh Sect., A 79, 107-129 (1977/78)
    • (1977) Proc. Roy. Soc. Edinburgh Sect., A , vol.79 , pp. 107-129
    • Attouch, H.1    Damlamian, A.2
  • 7
    • 67749139722 scopus 로고    scopus 로고
    • On p-harmonic map heat flows for 1 p < ∞ and their finite element approximations
    • 10.1137/070680825 2466164
    • J.W. Barrett X. Feng A. Prohl 2008 On p-harmonic map heat flows for 1 p < ∞ and their finite element approximations SIAM J. Math. Anal. 40 1471 1498 10.1137/070680825 2466164
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 1471-1498
    • Barrett, J.W.1    Feng, X.2    Prohl, A.3
  • 9
    • 0039455666 scopus 로고    scopus 로고
    • Approximation to driven motion by crystalline curvature in two dimensions
    • 0979.53075 1769163
    • G. Bellettini R. Goglione M. Novaga 2000 Approximation to driven motion by crystalline curvature in two dimensions Adv. Math. Sci. Appl. 10 467 493 0979.53075 1769163
    • (2000) Adv. Math. Sci. Appl. , vol.10 , pp. 467-493
    • Bellettini, G.1    Goglione, R.2    Novaga, M.3
  • 12
    • 84971505912 scopus 로고    scopus 로고
    • Facet-breaking for three-dimensional crystals evolving by mean curvature
    • 0934.49023 10.4171/IFB/3 1865105
    • G. Bellettini M. Novaga M. Paolini 1999 Facet-breaking for three-dimensional crystals evolving by mean curvature Interfaces Free Bound. 1 39 55 0934.49023 10.4171/IFB/3 1865105
    • (1999) Interfaces Free Bound. , vol.1 , pp. 39-55
    • Bellettini, G.1    Novaga, M.2    Paolini, M.3
  • 13
    • 85016548547 scopus 로고    scopus 로고
    • Characterization of facet breaking for nonsmooth mean curvature flow in the convex case
    • G. Bellettini M. Novaga M. Paolini 2001 Characterization of facet breaking for nonsmooth mean curvature flow in the convex case Interfaces Free Bound. 3 415 446 0989.35127 10.4171/IFB/47 1869587 (Pubitemid 33360839)
    • (2001) Interfaces and free boundaries , vol.3 , Issue.4 , pp. 415-446
    • Bellettini, G.1    Novaga, M.2    Paolini, M.3
  • 14
    • 0035631880 scopus 로고    scopus 로고
    • On a crystalline variational problem, part II: B V regularity and structure of minimizers on facets
    • G. Bellettini M. Novaga M. Paolini 2001 On a crystalline variational problem. Part II: BV regularity and structure of minimizers on facets Arch. Ration. Mech. Anal. 157 193 217 0976.58017 10.1007/s002050100126 1826965 (Pubitemid 33582049)
    • (2001) Archive for Rational Mechanics and Analysis , vol.157 , Issue.3 , pp. 193-217
    • Bellettini, G.1    Novaga, M.2    Paolini, M.3
  • 15
    • 0039992070 scopus 로고    scopus 로고
    • Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff
    • A.J. Bernoff A.L. Bertozzi T.P. Witelski 1998 Axisymmetric surface diffusion: dynamics and stability of self-similar pinchoff J. Stat. Phys. 93 725 776 0951.74007 10.1023/B:JOSS.0000033251.81126.af 1666581 (Pubitemid 128362490)
    • (1998) Journal of Statistical Physics , vol.93 , Issue.3-4 , pp. 725-776
    • Bernoff, A.J.1    Bertozzi, A.L.2    Witelski, T.P.3
  • 16
    • 0041510122 scopus 로고
    • Une application de la symétrisation de Steiner aux équations hyperboliques : la méthode de transport et écroulement
    • 0459.35006 614670
    • Y. Brenier 1981 Une application de la symétrisation de Steiner aux équations hyperboliques : la méthode de transport et écroulement C. R. Acad. Sci. Paris Sér I. Math. 292 563 566 0459.35006 614670
    • (1981) C. R. Acad. Sci. Paris sér I. Math. , vol.292 , pp. 563-566
    • Brenier, Y.1
  • 17
    • 0000337570 scopus 로고
    • Résolution déquations dévolution quasilinéaires en dimention N despace à laide déquations linéaires en dimension N + 1
    • 0549.35055 10.1016/0022-0396(83)90067-0 723577
    • Y. Brenier 1983 Résolution déquations dévolution quasilinéaires en dimention N despace à laide déquations linéaires en dimension N + 1 J. Differ. Equ. 50 375 390 0549.35055 10.1016/0022-0396(83)90067-0 723577
    • (1983) J. Differ. Equ. , vol.50 , pp. 375-390
    • Brenier, Y.1
  • 18
    • 59849111345 scopus 로고    scopus 로고
    • 2 formulation of multidimensional scalar conservation laws
    • 1180.35346 10.1007/s00205-009-0214-0 2506069
    • 2 formulation of multidimensional scalar conservation laws Arch. Ration. Mech. Anal. 193 1 19 1180.35346 10.1007/s00205-009-0214-0 2506069
    • (2009) Arch. Ration. Mech. Anal. , vol.193 , pp. 1-19
    • Brenier, Y.1
  • 20
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • DOI 10.1007/s002110050258
    • A. Chambolle P.-L. Lions 1997 Image recovery via total variation minimization and related problems Numer. Math. 76 167 188 0874.68299 10.1007/s002110050258 1440119 (Pubitemid 127056405)
    • (1997) Numerische Mathematik , vol.76 , Issue.2 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 21
    • 0030488511 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature
    • J.W. Cahn C.M. Elliott A. Novick-Cohen 1996 The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature Eur. J. Appl. Math. 7 287 301 0861.35039 10.1017/ S0956792500002369 1401172 (Pubitemid 126416019)
    • (1996) European Journal of Applied Mathematics , vol.7 , Issue.3 , pp. 287-301
    • Cahn, J.W.1    Elliott, C.M.2    Novick-Cohen, A.3
  • 22
    • 0028409294 scopus 로고
    • Surface motion by surface diffusion
    • 10.1016/0956-7151(94)90123-6
    • J.W. Cahn J. Taylor 1994 Surface motion by surface diffusion Acta Metall. Mater. 42 1045 1063 10.1016/0956-7151(94)90123-6
    • (1994) Acta Metall. Mater. , vol.42 , pp. 1045-1063
    • Cahn, J.W.1    Taylor, J.2
  • 23
    • 0033407951 scopus 로고    scopus 로고
    • Entropy solutions for nonlinear degenerate problems
    • 0935.35056 10.1007/s002050050152 1709116
    • J. Carrillo 1999 Entropy solutions for nonlinear degenerate problems Arch. Ration. Mech. Anal. 147 269 361 0935.35056 10.1007/s002050050152 1709116
    • (1999) Arch. Ration. Mech. Anal. , vol.147 , pp. 269-361
    • Carrillo, J.1
  • 24
    • 0000381088 scopus 로고
    • Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces
    • 10.1016/0956-7151(95)00134-H
    • W.C. Carter A.R. Roosen J.W. Cahn J.E. Taylor 1995 Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces Acta. Metall. Mater. 43 4309 4323 10.1016/0956-7151(95)00134-H
    • (1995) Acta. Metall. Mater. , vol.43 , pp. 4309-4323
    • Carter, W.C.1    Roosen, A.R.2    Cahn, J.W.3    Taylor, J.E.4
  • 25
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • 0696.35087 1100211
    • Y.-G. Chen Y. Giga S. Goto 1991 Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations J. Differ. Geom. 33 749 786 0696.35087 1100211
    • (1991) J. Differ. Geom. , vol.33 , pp. 749-786
    • Chen, Y.-G.1    Giga, Y.2    Goto, S.3
  • 26
    • 23044456037 scopus 로고    scopus 로고
    • A blow-up criterion for the curve shortening flow by surface diffusion
    • 1054.35105 1962022
    • K.-S. Chou 2003 A blow-up criterion for the curve shortening flow by surface diffusion Hokkaido Math. J. 32 1 19 1054.35105 1962022
    • (2003) Hokkaido Math. J. , vol.32 , pp. 1-19
    • Chou, K.-S.1
  • 28
    • 84967708673 scopus 로고
    • Users guide to viscosity solutions of second order partial differential equations
    • 0755.35015 10.1090/S0273-0979-1992-00266-5 1118699
    • M. Crandall H. Ishii P.-L. Lions 1992 Users guide to viscosity solutions of second order partial differential equations Bull. Am. Math. Soc. 27 1 67 0755.35015 10.1090/S0273-0979-1992-00266-5 1118699
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.-L.3
  • 29
    • 10844220570 scopus 로고    scopus 로고
    • Losing a graph with surface diffusion
    • 0993.35042 1844821
    • C.M. Elliott S. Maier-Paape 2001 Losing a graph with surface diffusion Hokkaido Math. J. 30 297 305 0993.35042 1844821
    • (2001) Hokkaido Math. J. , vol.30 , pp. 297-305
    • Elliott, C.M.1    Maier-Paape, S.2
  • 30
    • 35648988404 scopus 로고    scopus 로고
    • -1 fidelity model for decomposing an image into cartoon plus texture
    • 1148.35329 10.3934/cpaa.2007.6.917 2341813
    • -1 fidelity model for decomposing an image into cartoon plus texture Commun. Pure Appl. Anal. 6 917 936 1148.35329 10.3934/cpaa.2007.6.917 2341813
    • (2007) Commun. Pure Appl. Anal. , vol.6 , pp. 917-936
    • Elliott, C.M.1    Smitheman, S.A.2
  • 31
    • 67651173225 scopus 로고    scopus 로고
    • -1 fidelity model for decomposing an image into cartoon plus texture
    • 1169.94003 10.1093/imanum/drn025 2520163
    • -1 fidelity model for decomposing an image into cartoon plus texture IMA J. Numer. Anal. 29 651 689 1169.94003 10.1093/imanum/drn025 2520163
    • (2009) IMA J. Numer. Anal. , vol.29 , pp. 651-689
    • Elliott, C.M.1    Smitheman, S.A.2
  • 32
    • 0032379074 scopus 로고    scopus 로고
    • The surface diffusion flow for immersed hypersurfaces
    • 0912.35161 10.1137/S0036141097320675 1638074
    • J. Escher U.F. Mayer G. Simonett 1998 The surface diffusion flow for immersed hypersurfaces SIAM J. Math. Anal. 29 1419 1433 0912.35161 10.1137/S0036141097320675 1638074
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1419-1433
    • Escher, J.1    Mayer, U.F.2    Simonett, G.3
  • 33
    • 0000107438 scopus 로고    scopus 로고
    • Fast/Slow Diffusion and Collapsing Sandpiles
    • DOI 10.1006/jdeq.1997.3243, PII S0022039697932435
    • L.C. Evans M. Feldman R.F. Gariepy 1997 Fast/slow diffusion and collapsing sandpiles J. Differ. Equ. 137 166 209 0879.35019 10.1006/jdeq.1997. 3243 1451539 (Pubitemid 127343455)
    • (1997) Journal of Differential Equations , vol.137 , Issue.1 , pp. 166-209
    • Evans, L.C.1    Feldman, M.2    Gariepy, R.F.3
  • 34
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature, i
    • 0726.53029 1100206
    • L.C. Evans J. Spruck 1991 Motion of level sets by mean curvature, I J. Differ. Geom. 33 635 681 0726.53029 1100206
    • (1991) J. Differ. Geom. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 35
    • 0002227665 scopus 로고    scopus 로고
    • Motion of a graph by nonsmooth weighted curvature
    • Lakshmikantham, V. (ed.) Walter de Gruyter, Berlin
    • Fukui, T., Giga, Y.: Motion of a graph by nonsmooth weighted curvature. In: Lakshmikantham, V. (ed.) World Congress of Nonlinear Analysts 92, vol. I, pp. 47-56. Walter de Gruyter, Berlin (1996)
    • (1996) World Congress of Nonlinear Analysts 92 , vol.1 , pp. 47-56
    • Fukui, T.1    Giga, Y.2
  • 37
    • 0032391468 scopus 로고    scopus 로고
    • Evolving Graphs by Singular Weighted Curvature
    • DOI 10.1007/s002050050075
    • M.-H. Giga Y. Giga 1998 Evolving graphs by singular weighted curvature Arch. Ration. Mech. Anal. 141 117 198 0896.35069 10.1007/s002050050075 1615520 (Pubitemid 128051377)
    • (1998) Archive for Rational Mechanics and Analysis , vol.141 , Issue.2 , pp. 117-198
    • Giga, M.-H.1    Giga, Y.2
  • 38
    • 0009423784 scopus 로고    scopus 로고
    • A subdifferential interpretation of crystalline motion under nonuniform driving force
    • Chen, W.-X., Hu, S.-C. (eds.) Springfield Missouri Dynamical Systems and Differential Equations, Southwest Missouri University
    • Giga, M.-H., Giga, Y.: A subdifferential interpretation of crystalline motion under nonuniform driving force. In: Chen, W.-X., Hu, S.-C. (eds.) Proceedings of the International Conference in Dynamical Systems and Differential Equations, Springfield Missouri, (1996). Dynamical Systems and Differential Equations, Southwest Missouri University, vol. 1, pp. 276-287 (1998)
    • (1996) Proceedings of the International Conference in Dynamical Systems and Differential Equations , vol.1 , pp. 276-287
    • Giga, M.-H.1    Giga, Y.2
  • 39
    • 0001696566 scopus 로고    scopus 로고
    • Stability for evolving graphs by nonlocal weighted curvature
    • 0924.35177 10.1080/03605309908821419 1671993
    • M.-H. Giga Y. Giga 1999 Stability for evolving graphs by nonlocal weighted curvature Commun. Partial Differ. Equ. 24 109 184 0924.35177 10.1080/03605309908821419 1671993
    • (1999) Commun. Partial Differ. Equ. , vol.24 , pp. 109-184
    • Giga, M.-H.1    Giga, Y.2
  • 40
    • 0035602118 scopus 로고    scopus 로고
    • Generalized motion by nonlocal curvature in the plane
    • 1004.35075 10.1007/s002050100154 1860050
    • M.-H. Giga Y. Giga 2001 Generalized motion by nonlocal curvature in the plane Arch. Ration. Mech. Anal. 159 295 333 1004.35075 10.1007/s002050100154 1860050
    • (2001) Arch. Ration. Mech. Anal. , vol.159 , pp. 295-333
    • Giga, M.-H.1    Giga, Y.2
  • 41
    • 79952008817 scopus 로고    scopus 로고
    • A PDE approach for motion of phase-boundaries by a singular interfacial energy
    • Funaki, T., Osada, H. (eds.) Math. Soc. Japan
    • Giga, M.-H., Giga, Y.: A PDE approach for motion of phase-boundaries by a singular interfacial energy. In: Funaki, T., Osada, H. (eds.) Stochastic Analysis on Large Scale Interacting System. Advanced Studies in Pure Math., vol. 39, pp. 213-232. Math. Soc. Japan (2004)
    • (2004) Stochastic Analysis on Large Scale Interacting System. Advanced Studies in Pure Math. , vol.39 , pp. 213-232
    • Giga, M.-H.1    Giga, Y.2
  • 43
    • 33746117969 scopus 로고    scopus 로고
    • Self-similar expanding solutions in a sector for a crystalline flow
    • DOI 10.1137/040614372
    • M.-H. Giga Y. Giga H. Hontani 2005 Self-similar expanding solutions in a sector for a crystalline flow SIAM J. Math. Anal. 37 1207 1226 10.1137/040614372 2192293 (Pubitemid 44085077)
    • (2005) SIAM Journal on Mathematical Analysis , vol.37 , Issue.4 , pp. 1207-1226
    • Giga, M.-H.1    Giga, Y.2    Hontani, H.3
  • 45
    • 0141901866 scopus 로고    scopus 로고
    • Very singular diffusion equations
    • Maruyama, M., Sunada, T. (eds.) Taniguchi Conference on Mathematics Nara 98
    • Giga, M.-H., Giga, Y., Kobayashi, R.: Very singular diffusion equations. In: Maruyama, M., Sunada, T. (eds.) Adv. Studies in Pure Math., vol. 31, pp. 93-125. Taniguchi Conference on Mathematics Nara 98 (2001)
    • (2001) Adv. Studies in Pure Math. , vol.31 , pp. 93-125
    • Giga, M.-H.1    Giga, Y.2    Kobayashi, R.3
  • 47
    • 33644505340 scopus 로고    scopus 로고
    • Anisotropic curvature effects in interface dynamics
    • 2019167 Translation from Sūgaku 52:113-127
    • Y. Giga 2003 Anisotropic curvature effects in interface dynamics Sugaku Expositions 16 135 152 2019167 Translation from Sūgaku 52:113-127
    • (2003) Sugaku Expositions , vol.16 , pp. 135-152
    • Giga, Y.1
  • 48
    • 3042832328 scopus 로고    scopus 로고
    • Singular diffusivity-facets, shocks and more
    • Hill, J.M., Moore, R. (eds.) ICIAM 2003 Sydney. SIAM, Philadelphia
    • Giga, Y.: Singular diffusivity-facets, shocks and more. In: Hill, J.M., Moore, R. (eds.) Applied Math Entering the 21th Century, pp. 121-138. ICIAM 2003 Sydney. SIAM, Philadelphia (2004)
    • (2004) Applied Math Entering the 21th Century , pp. 121-138
    • Giga, Y.1
  • 49
    • 0036100668 scopus 로고    scopus 로고
    • Viscosity Solutions with Shocks
    • DOI 10.1002/cpa.3015
    • Y. Giga 2002 Viscosity solutions with shocks Commun. Pure Appl. Math. 55 431 480 1028.35044 10.1002/cpa.3015 1879195 (Pubitemid 37239308)
    • (2002) Communications on Pure and Applied Mathematics , vol.55 , Issue.4 , pp. 431-480
    • Giga, Y.1
  • 52
    • 77950142167 scopus 로고    scopus 로고
    • Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary
    • 1183.49028 10.3934/dcds.2010.26.493 2556496
    • Y. Giga P. Górka P. Rybka 2010 Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary Discrete Contin. Dyn. Syst. 26 493 519 1183.49028 10.3934/dcds.2010.26.493 2556496
    • (2010) Discrete Contin. Dyn. Syst. , vol.26 , pp. 493-519
    • Giga, Y.1    Górka, P.2    Rybka, P.3
  • 53
    • 0011541312 scopus 로고    scopus 로고
    • On pinching of curves moved by surface diffusion
    • 0894.35049 1626705
    • Y. Giga K. Ito 1998 On pinching of curves moved by surface diffusion Commun. Appl. Anal. 2 393 405 0894.35049 1626705
    • (1998) Commun. Appl. Anal. , vol.2 , pp. 393-405
    • Giga, Y.1    Ito, K.2
  • 54
    • 0007270815 scopus 로고    scopus 로고
    • Loss of Convexity of Simple Closed Curves Moved by Surface Diffusion
    • Topics in Nonlinear Analysis: The Herbert Amann Anniversary Volume
    • Giga, Y., Ito, K.: Loss of convexity of simple closed curves moved by surface diffusion. In: Escher, J., Simonett, G. (eds.) Topics in Nonlinear Analysis, The Herbert Amann Aniversary Volume. Progress in Nonlinear Differential Equations, vol. 35, pp. 305-320. Birkhäuser, Basel (1999) (Pubitemid 128158396)
    • (1999) Progress in nonlinear differential equations and their applications , vol.35 , pp. 305-320
    • Giga, Y.1    Ito, K.2
  • 55
    • 9344242944 scopus 로고    scopus 로고
    • Local solvability of a constrained gradient system of total variation
    • DOI 10.1155/S1085337504311048
    • Giga, Y., Kashima, Y., Yamazaki, N.: Local solvability of a constrained gradient system of total variation. Abstr. Appl. Anal., pp. 651-682 (2004) (Pubitemid 39557955)
    • (2004) Abstract and Applied Analysis , vol.2004 , Issue.8 , pp. 651-682
    • Giga, Y.1    Kashima, Y.2    Yamazaki, N.3
  • 56
    • 9344266553 scopus 로고    scopus 로고
    • On constrained equations with singular diffusivity
    • 1058.58006 2074751
    • Y. Giga R. Kobayashi 2003 On constrained equations with singular diffusivity Methods Appl. Anal. 10 253 277 1058.58006 2074751
    • (2003) Methods Appl. Anal. , vol.10 , pp. 253-277
    • Giga, Y.1    Kobayashi, R.2
  • 57
    • 79952007609 scopus 로고    scopus 로고
    • Scale-invariant extinction time estimates for some singular diffusion equations
    • (to appear)
    • Giga, Y., Kohn, R.V.: Scale-invariant extinction time estimates for some singular diffusion equations. Discrete Contin. Dyn. Syst. (to appear)
    • Discrete Contin. Dyn. Syst.
    • Giga, Y.1    Kohn, V.R.2
  • 58
    • 43949105740 scopus 로고    scopus 로고
    • On breakdown of solutions of a constrained gradient system of total variation, Bol
    • 1064.35084 2094791
    • Y. Giga H. Kuroda 2004 On breakdown of solutions of a constrained gradient system of total variation, Bol Soc. Parana. Mat. (3) 22 9 20 1064.35084 2094791
    • (2004) Soc. Parana. Mat. (3) , vol.22 , pp. 9-20
    • Giga, Y.1    Kuroda, H.2
  • 59
    • 84972568146 scopus 로고
    • A kinetic construction of slobal solutions of first order quasilinear equations
    • 0519.35053 10.1215/S0012-7094-83-05022-6 705037
    • Y. Giga T. Miyakawa 1983 A kinetic construction of slobal solutions of first order quasilinear equations Duke Math. J. 50 505 515 0519.35053 10.1215/S0012-7094-83-05022-6 705037
    • (1983) Duke Math. J. , vol.50 , pp. 505-515
    • Giga, Y.1    Miyakawa, T.2
  • 60
    • 1542740899 scopus 로고
    • A kinetic approach to general first order quasilinear equations
    • 10.1090/S0002-9947-1985-0768737-9 768737
    • Y. Giga T. Miyakawa S. Oharu 1987 A kinetic approach to general first order quasilinear equations Trans. Am. Math. Soc. 287 723 743 10.1090/S0002-9947-1985-0768737-9 768737
    • (1987) Trans. Am. Math. Soc. , vol.287 , pp. 723-743
    • Giga, Y.1    Miyakawa, T.2    Oharu, S.3
  • 61
    • 33750012063 scopus 로고    scopus 로고
    • On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations
    • Y. Giga T. Ohtsuka R. Schätzle 2006 On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations Interfaces Free Bound. 8 317 348 1106.35060 10.4171/IFB/146 2273232 (Pubitemid 44568614)
    • (2006) Interfaces and Free Boundaries , vol.8 , Issue.3 , pp. 317-348
    • Giga, Y.1    Ohtsuka, T.2    Schatzle, R.3
  • 62
    • 84867961471 scopus 로고    scopus 로고
    • Facet bending in the driven crystalline curvature flow in the plane
    • 1146.53037 10.1007/s12220-007-9004-9 2365670
    • Y. Giga P. Rybka 2008 Facet bending in the driven crystalline curvature flow in the plane J. Geom. Anal. 18 109 147 1146.53037 10.1007/s12220-007-9004-9 2365670
    • (2008) J. Geom. Anal. , vol.18 , pp. 109-147
    • Giga, Y.1    Rybka, P.2
  • 63
    • 59649106751 scopus 로고    scopus 로고
    • Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term
    • 1183.53061 10.1016/j.jde.2009.01.009 2498842
    • Y. Giga P. Rybka 2009 Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term J. Differ. Equ. 246 2264 2303 1183.53061 10.1016/j.jde.2009.01.009 2498842
    • (2009) J. Differ. Equ. , vol.246 , pp. 2264-2303
    • Giga, Y.1    Rybka, P.2
  • 66
    • 0000667207 scopus 로고
    • An evolution problem for linear growth functionals
    • 0811.35061 10.1080/03605309408821076 1301176
    • R. Hardt X. Zhou 1994 An evolution problem for linear growth functionals Commun. Partial Differ. Equ. 19 1879 1907 0811.35061 10.1080/03605309408821076 1301176
    • (1994) Commun. Partial Differ. Equ. , vol.19 , pp. 1879-1907
    • Hardt, R.1    Zhou, X.2
  • 67
    • 67249097145 scopus 로고    scopus 로고
    • Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures
    • 1166.53035 10.1512/iumj.2009.58.3515 2514391
    • Y. He H. Li H. Ma J. Ge 2009 Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures Indiana Univ. Math. J. 58 853 868 1166.53035 10.1512/iumj.2009.58.3515 2514391
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 853-868
    • He, Y.1    Li, H.2    Ma, H.3    Ge, J.4
  • 68
    • 63949084100 scopus 로고    scopus 로고
    • Anisotropic version of a theorem of H. Hopf
    • 1168.53028 10.1007/s10455-008-9133-9 2495974
    • Y. He H. Li 2009 Anisotropic version of a theorem of H. Hopf Ann. Glob. Anal. Geom. 35 243 247 1168.53028 10.1007/s10455-008-9133-9 2495974
    • (2009) Ann. Glob. Anal. Geom. , vol.35 , pp. 243-247
    • He, Y.1    Li, H.2
  • 69
    • 48249088009 scopus 로고    scopus 로고
    • Motion of non-convex polygons by crystalline curvature and almost convexity phenomena
    • 1155.53033 10.1007/BF03167521 2431681
    • T. Ishiwata 2008 Motion of non-convex polygons by crystalline curvature and almost convexity phenomena Jpn. J. Indust. Appl. Math. 25 233 253 1155.53033 10.1007/BF03167521 2431681
    • (2008) Jpn. J. Indust. Appl. Math. , vol.25 , pp. 233-253
    • Ishiwata, T.1
  • 71
    • 84867942278 scopus 로고    scopus 로고
    • A phase-field model of grain boundary motion
    • 1199.35138 10.1007/s10492-008-0035-8 2469586
    • A. Ito N. Kenmochi N. Yamazaki 2008 A phase-field model of grain boundary motion Appl. Math. 53 433 454 1199.35138 10.1007/s10492-008-0035-8 2469586
    • (2008) Appl. Math. , vol.53 , pp. 433-454
    • Ito, A.1    Kenmochi, N.2    Yamazaki, N.3
  • 72
    • 79952004294 scopus 로고    scopus 로고
    • Weak solutions of grain boundary motion model with singularity
    • 1183.35159 2548486
    • A. Ito N. Kenmochi N. Yamazaki 2009 Weak solutions of grain boundary motion model with singularity Rend. Mat. Appl. (7) 29 51 63 1183.35159 2548486
    • (2009) Rend. Mat. Appl. (7) , vol.29 , pp. 51-63
    • Ito, A.1    Kenmochi, N.2    Yamazaki, N.3
  • 73
    • 0033245879 scopus 로고    scopus 로고
    • Equations with singular diffusivity
    • 0952.74014 10.1023/A:1004570921372 1712447
    • R. Kobayashi Y. Giga 1999 Equations with singular diffusivity J. Stat. Phys. 95 1187 1220 0952.74014 10.1023/A:1004570921372 1712447
    • (1999) J. Stat. Phys. , vol.95 , pp. 1187-1220
    • Kobayashi, R.1    Giga, Y.2
  • 74
    • 0346053688 scopus 로고    scopus 로고
    • A continuum model of grain boundaries
    • 0956.35123 10.1016/S0167-2789(00)00023-3 1752970
    • R. Kobayashi J.A. Warren W.C. Carter 2000 A continuum model of grain boundaries Physica D 140 141 150 0956.35123 10.1016/S0167-2789(00)00023-3 1752970
    • (2000) Physica D , vol.140 , pp. 141-150
    • Kobayashi, R.1    Warren, J.A.2    Carter, W.C.3
  • 75
    • 78649937008 scopus 로고    scopus 로고
    • A subdifferential formulation of fourth order singular diffusion equations
    • 1067.35039 2083617
    • Y. Kashima 2004 A subdifferential formulation of fourth order singular diffusion equations Adv. Math. Sci. Appl. 14 49 74 1067.35039 2083617
    • (2004) Adv. Math. Sci. Appl. , vol.14 , pp. 49-74
    • Kashima, Y.1
  • 76
    • 34250215696 scopus 로고    scopus 로고
    • Characterization of Cheeger sets for convex subsets of the plane
    • 1133.52002 10.2140/pjm.2006.225.103 2233727
    • B. Kawohl Th. Lachand-Robert 2006 Characterization of Cheeger sets for convex subsets of the plane Pac. J. Math. 225 103 118 1133.52002 10.2140/pjm.2006.225.103 2233727
    • (2006) Pac. J. Math. , vol.225 , pp. 103-118
    • Kawohl, B.1    Lachand-Robert, Th.2
  • 77
    • 34547962314 scopus 로고    scopus 로고
    • Dirichlet problems for the 1-Laplace operator, including the eigenvalue problem
    • 1146.35023 10.1142/S0219199707002514 2348842
    • B. Kawohl F. Schuricht 2007 Dirichlet problems for the 1-Laplace operator, including the eigenvalue problem Commun. Contemp. Math. 9 515 543 1146.35023 10.1142/S0219199707002514 2348842
    • (2007) Commun. Contemp. Math. , vol.9 , pp. 515-543
    • Kawohl, B.1    Schuricht, F.2
  • 79
    • 33644591594 scopus 로고    scopus 로고
    • A deterministic-control-based approach to motion by curvature
    • 05023699 10.1002/cpa.20101 2200259
    • R.V. Kohn S. Serfaty 2006 A deterministic-control-based approach to motion by curvature Commun. Pure Appl. Math. 59 344 407 05023699 10.1002/cpa.20101 2200259
    • (2006) Commun. Pure Appl. Math. , vol.59 , pp. 344-407
    • Kohn, R.V.1    Serfaty, S.2
  • 80
    • 77956472549 scopus 로고    scopus 로고
    • A deterministic-control-based approach to fully nonlinear parabolic and elliptic equations
    • 05782520 10.1002/cpa.20336 2681474
    • R.V. Kohn S. Serfaty 2010 A deterministic-control-based approach to fully nonlinear parabolic and elliptic equations Commun. Pure. Appl. Math. 63 1298 1350 05782520 10.1002/cpa.20336 2681474
    • (2010) Commun. Pure. Appl. Math. , vol.63 , pp. 1298-1350
    • Kohn, R.V.1    Serfaty, S.2
  • 81
    • 31644447816 scopus 로고    scopus 로고
    • Geometry and stability of surfaces with constant anisotropic mean curvature
    • M. Koiso B. Palmer 2005 Geometry and stability of surfaces with constant anisotropic mean curvature Indiana Univ. Math. J. 54 1817 1852 1120.58010 10.1512/iumj.2005.54.2613 2189687 (Pubitemid 43170698)
    • (2005) Indiana University Mathematics Journal , vol.54 , Issue.6 , pp. 1817-1852
    • Koiso, M.1    Palmer, B.2
  • 82
    • 33644517880 scopus 로고    scopus 로고
    • Stability of anisotropic capillary surfaces between two parallel planes
    • DOI 10.1007/s00526-005-0336-7
    • M. Koiso B. Palmer 2006 Stability of anisotropic capillary surfaces between two parallel planes Calc. Var. Partial Differ. Equ. 25 275 298 1095.76019 10.1007/s00526-005-0336-7 2201674 (Pubitemid 43296597)
    • (2006) Calculus of Variations and Partial Differential Equations , vol.25 , Issue.3 , pp. 275-298
    • Koiso, M.1    Palmer, B.2
  • 83
    • 77954606739 scopus 로고    scopus 로고
    • Anisotropic umblic points and Hopfs Theorem for surface with constant anisotropic mean curvature
    • 05735724 10.1512/iumj.2010.59.4164 2666473
    • M. Koiso B. Palmer 2010 Anisotropic umblic points and Hopfs Theorem for surface with constant anisotropic mean curvature Indiana Univ. Math. J. 59 79 90 05735724 10.1512/iumj.2010.59.4164 2666473
    • (2010) Indiana Univ. Math. J. , vol.59 , pp. 79-90
    • Koiso, M.1    Palmer, B.2
  • 84
    • 84972544461 scopus 로고
    • Nonlinear semi-groups in Hilbert space
    • 0163.38302 10.2969/jmsj/01940493
    • Y. Kōmura 1967 Nonlinear semi-groups in Hilbert space J. Math. Soc. Jpn. 19 493 507 0163.38302 10.2969/jmsj/01940493
    • (1967) J. Math. Soc. Jpn. , vol.19 , pp. 493-507
    • Komura, Y.1
  • 85
    • 84956238079 scopus 로고
    • First order quasilinear equations with several independent variables
    • 0215.16203 10.1070/SM1970v010n02ABEH002156
    • S.N. Kruzhkov 1970 First order quasilinear equations with several independent variables Math. USSR-Sb. 10 217 243 0215.16203 10.1070/ SM1970v010n02ABEH002156
    • (1970) Math. USSR-Sb. , vol.10 , pp. 217-243
    • Kruzhkov, S.N.1
  • 86
    • 84972583953 scopus 로고
    • Construction of solutions of a semilinear paraboric equation with the aid of the linear Boltzmann equation
    • 0562.35047 764453
    • T. Miyakawa 1984 Construction of solutions of a semilinear paraboric equation with the aid of the linear Boltzmann equation Hiroshima Math. J. 14 299 310 0562.35047 764453
    • (1984) Hiroshima Math. J. , vol.14 , pp. 299-310
    • Miyakawa, T.1
  • 87
    • 17444392809 scopus 로고    scopus 로고
    • The anisotropic total variation flow
    • DOI 10.1007/s00208-004-0624-0
    • J.S. Moll 2005 The anisotropic total variation flow Math. Ann. 332 177 218 1109.35061 10.1007/s00208-004-0624-0 2139257 (Pubitemid 40550203)
    • (2005) Mathematische Annalen , vol.332 , Issue.1 , pp. 177-218
    • Moll, J.S.1
  • 88
    • 14644408068 scopus 로고    scopus 로고
    • Planar Wulff shape is unique equilibrium
    • DOI 10.1090/S0002-9939-04-07661-0, PII S0002993904076610
    • F. Morgan 2005 Planar Wulff shape is unique equilibrium Proc. Am. Math. Soc. 133 809 813 1071.49025 10.1090/S0002-9939-04-07661-0 (Pubitemid 40322771)
    • (2005) Proceedings of the American Mathematical Society , vol.133 , Issue.3 , pp. 809-813
    • Morgan, F.1
  • 89
    • 48249122348 scopus 로고    scopus 로고
    • A new look at equilibria in Stefan-type problems in the plane
    • 1145.53033 10.1137/060677124 2368896
    • P.B. Mucha P. Rybka 2007 A new look at equilibria in Stefan-type problems in the plane SIAM J. Math. Anal. 39 1120 1134 1145.53033 10.1137/060677124 2368896
    • (2007) SIAM J. Math. Anal. , vol.39 , pp. 1120-1134
    • Mucha, P.B.1    Rybka, P.2
  • 90
    • 21544450961 scopus 로고
    • Theory of thermal grooving
    • 10.1063/1.1722742
    • W.W. Mullins 1957 Theory of thermal grooving J. Appl. Phys. 28 333 339 10.1063/1.1722742
    • (1957) J. Appl. Phys. , vol.28 , pp. 333-339
    • Mullins, W.W.1
  • 93
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithm
    • 0780.49028 10.1016/0167-2789(92)90242-F
    • L. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithm Physica D 60 259 268 0780.49028 10.1016/0167-2789(92)90242-F
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 96
    • 10044229236 scopus 로고    scopus 로고
    • Stability analysis for Allen-Cahn type equation associated with the total variation energy
    • 02132831 2101878
    • K. Shirakawa M. Kimura 2005 Stability analysis for Allen-Cahn type equation associated with the total variation energy Nonlinear Anal. 60 257 282 02132831 2101878
    • (2005) Nonlinear Anal. , vol.60 , pp. 257-282
    • Shirakawa, K.1    Kimura, M.2
  • 97
    • 0001965304 scopus 로고
    • Surface dynamics below the roughening temperature
    • 10.1051/jp1:1993117
    • H. Spohn 1993 Surface dynamics below the roughening temperature J. Phys. I. France 3 69 81 10.1051/jp1:1993117
    • (1993) J. Phys. I. France , vol.3 , pp. 69-81
    • Spohn, H.1
  • 98
    • 0033893218 scopus 로고    scopus 로고
    • Diffusion of general data on non-flat manifolds via harmonic maps theory: The direction diffusion case
    • DOI 10.1023/A:1008152115986
    • B. Tang G. Sapiro V. Caselles 2000 Diffusion of general data on non-flat manifold via harmonic map theory; the direction diffusion case Int. J. Comput. Vis. 36 149 161 10.1023/A:1008152115986 (Pubitemid 30588072)
    • (2000) International Journal of Computer Vision , vol.36 , Issue.2 , pp. 149-161
    • Tang, B.1    Sapiro, G.2    Caselles, V.3
  • 99
    • 0000880047 scopus 로고
    • Constructions and conjectures in crystalline nondifferential geometry
    • Lawson, B., Tanenblat, K. (eds.) Pitman Monographs in Pure and Applied Math. Pitman, London
    • Taylor, J.: Constructions and conjectures in crystalline nondifferential geometry. In: Lawson, B., Tanenblat, K. (eds.) Differential Geometry. Proceedings of the Conference on Differential Geometry, Rio de Janeiro. Pitman Monographs in Pure and Applied Math., vol. 52, pp. 321-336. Pitman, London (1991)
    • (1991) Differential Geometry. Proceedings of the Conference on Differential Geometry, Rio de Janeiro , vol.52 , pp. 321-336
    • Taylor, J.1
  • 100
    • 0037235382 scopus 로고    scopus 로고
    • A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations
    • Y.-H.R. Tsai Y. Giga S. Osher 2003 A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations Math. Comput. 72 159 181 1013.65088 1933817 (Pubitemid 36363856)
    • (2003) Mathematics of Computation , vol.71 , Issue.241 , pp. 159-181
    • Tsai, Y.-H.R.1    Giga, Y.2    Osher, S.3
  • 101
    • 1642503913 scopus 로고    scopus 로고
    • Numerical methods for p-harmonic flows and applications to image processing
    • 1035.65065 10.1137/S0036142901396715 1974176
    • L. Vese S. Osher 2002 Numerical methods for p-harmonic flows and applications to image processing SIAM J. Numer. Anal. 40 2085 2104 1035.65065 10.1137/S0036142901396715 1974176
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 2085-2104
    • Vese, L.1    Osher, S.2
  • 102
    • 79952004443 scopus 로고    scopus 로고
    • BV-entropy solutions to nonlinear strongly degenerate parabolic equations
    • 05735006 2650587
    • H. Watanabe S. Oharu 2010 BV-entropy solutions to nonlinear strongly degenerate parabolic equations Adv. Differ. Equ. 15 757 800 05735006 2650587
    • (2010) Adv. Differ. Equ. , vol.15 , pp. 757-800
    • Watanabe, H.1    Oharu, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.