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Volumn 28, Issue 2, 1997, Pages 274-303

The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case

Author keywords

Anisotropic Allen Cahn equation; Double obstacle problem; Mean curvature flow; Viscosity solutions

Indexed keywords


EID: 0039386147     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095286733     Document Type: Article
Times cited : (22)

References (21)
  • 1
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • S. ALLEN AND J. CAHN, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metallurgica, 27 (1979), pp. 1084-1095.
    • (1979) Acta Metallurgica , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.2
  • 3
    • 84972530683 scopus 로고
    • Quasi-optimal error estimates for the mean-curvature flow with forcing term
    • G. BELLETINI AND M. PAOLINI, Quasi-optimal error estimates for the mean-curvature flow with forcing term, Differential Integral Equations, 8 (1995), pp. 735-752.
    • (1995) Differential Integral Equations , vol.8 , pp. 735-752
    • Belletini, G.1    Paolini, M.2
  • 4
    • 33645716070 scopus 로고
    • Anisotropic motion by mean curvature in the context of Finsler geometry
    • Universitá degli Studi di Milano, Milan, Italy, Hokkaido Math. J., to appear
    • G. BELLETINI AND M. PAOLINI, Anisotropic motion by mean curvature in the context of Finsler geometry, Quaderno 49, Universitá degli Studi di Milano, Milan, Italy, 1994; Hokkaido Math. J., to appear.
    • (1994) Quaderno , vol.49
    • Belletini, G.1    Paolini, M.2
  • 5
    • 0002252307 scopus 로고
    • Curvature dependent phase boundary motion and parabolic obstacle problems
    • W. Ni, L. Peletier, and J. L. Vasquez, eds., Springer-Verlag, Berlin
    • J. F. BLOWEY AND C. M. ELLIOTT, Curvature dependent phase boundary motion and parabolic obstacle problems, in Proc. IMA Workshop on Degenerate Diffusion, Vol. 47, W. Ni, L. Peletier, and J. L. Vasquez, eds., Springer-Verlag, Berlin, 1993, pp. 19-60.
    • (1993) Proc. IMA Workshop on Degenerate Diffusion , vol.47 , pp. 19-60
    • Blowey, J.F.1    Elliott, C.M.2
  • 6
    • 0001249829 scopus 로고
    • Generation and propagation of interface in reaction-diffusion equations
    • X. CHEN, Generation and propagation of interface in reaction-diffusion equations, J. Differential Equations, 96 (1992), pp. 116-141.
    • (1992) J. Differential Equations , vol.96 , pp. 116-141
    • Chen, X.1
  • 7
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y. CHEN, Y. GIGA, AND S. GOTO, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom., 33 (1991), pp. 749-786
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.1    Giga, Y.2    Goto, S.3
  • 8
    • 0037849059 scopus 로고
    • Asymptotics for a parabolic double obstacle problem
    • X. CHEN AND C. M. ELLIOTT, Asymptotics for a parabolic double obstacle problem, Proc. Roy. Soc. London Ser. A, 444 (1994), pp. 429-445.
    • (1994) Proc. Roy. Soc. London Ser. A , vol.444 , pp. 429-445
    • Chen, X.1    Elliott, C.M.2
  • 9
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. CRANDALL, H. ISHI, AND P.-L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), pp. 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishi, H.2    Lions, P.-L.3
  • 11
    • 21444458744 scopus 로고    scopus 로고
    • The limit of the anisotropic double-obstacle Allen-Cahn equation
    • to appear
    • C. M. ELLIOTT AND R. SCHÄTZLE, The limit of the anisotropic double-obstacle Allen-Cahn equation, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 126, to appear.
    • Proc. Roy. Soc. Edinburgh Sect. A , vol.126
    • Elliott, C.M.1    Schätzle, R.2
  • 12
    • 85033106218 scopus 로고    scopus 로고
    • The limit of the anisotropic double-obstacle Allen-Cahn equation with kinetic term
    • to appear
    • C. M. ELLIOTT, M. PAOLINI, AND R. SCHÄTZLE, The limit of the anisotropic double-obstacle Allen-Cahn equation with kinetic term, Math. Models Methods Appl. Sci., to appear.
    • Math. Models Methods Appl. Sci.
    • Elliott, C.M.1    Paolini, M.2    Schätzle, R.3
  • 13
    • 84990617538 scopus 로고
    • Phase transitions and generalized motion by mean curvature
    • L .C. EVANS, H. M. SONER, AND P. E. SOUGANIDIS, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math., XLV (1992), pp. 1097-1123.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 1097-1123
    • Evans, L.C.1    Soner, H.M.2    Souganidis, P.E.3
  • 16
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • L. MODICA, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., 98 (1987), pp. 123-142.
    • (1987) Arch. Rational Mech. Anal. , vol.98 , pp. 123-142
    • Modica, L.1
  • 17
  • 18
    • 85033071435 scopus 로고
    • Convergence of double obstacle problems to the geometric motions of fronts
    • Universitá degli Studi di Milano, Milan, Italy
    • R. H. NOCHETTO AND C. VERDI, Convergence of double obstacle problems to the geometric motions of fronts, Quaderno 39, Universitá degli Studi di Milano, Milan, Italy, 1994.
    • (1994) Quaderno , vol.39
    • Nochetto, R.H.1    Verdi, C.2
  • 19
    • 0000935065 scopus 로고
    • Motion of a set by the curvature of its boundary
    • H. M. SONER, Motion of a set by the curvature of its boundary, J. Differential Equations, 101 (1993), pp. 313-372.
    • (1993) J. Differential Equations , vol.101 , pp. 313-372
    • Soner, H.M.1
  • 20
    • 21844495223 scopus 로고
    • Linking anisotropic sharp and diffuse surface motion laws via gradient flows
    • J. E. TAYLOR AND J. W. CAHN, Linking anisotropic sharp and diffuse surface motion laws via gradient flows, J. Statist. Phys., 77 (1993), pp. 183-197.
    • (1993) J. Statist. Phys. , vol.77 , pp. 183-197
    • Taylor, J.E.1    Cahn, J.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.