메뉴 건너뛰기




Volumn 335, Issue 4, 2006, Pages 819-851

On the evolution governed by the infinity Laplacian

Author keywords

Infinity heat equation; Infinity Laplacian

Indexed keywords


EID: 33745590130     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-006-0766-3     Document Type: Article
Times cited : (73)

References (32)
  • 1
    • 0001457134 scopus 로고
    • Extension of functions satisfying Lipschitz conditions
    • Aronsson, G.: Extension of functions satisfying Lipschitz conditions. Ark. Mat. 6, 551-561 (1967)
    • (1967) Ark. Mat. , vol.6 , pp. 551-561
    • Aronsson, G.1
  • 6
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Chen, Y., Giga, Y., Goto, S.: Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom., 33, 749-786 (1991)
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.1    Giga, Y.2    Goto, S.3
  • 9
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall, M.G., Ishii, H., Lions, P.-L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27(1), 1-67 (1992)
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 10
    • 1642303113 scopus 로고    scopus 로고
    • Another way to say caloric
    • Crandall, M.G., Wang, P.-Y.: Another way to say caloric. J. Evol. Equ. 3(4), 653-672 (2004)
    • (2004) J. Evol. Equ. , vol.3 , Issue.4 , pp. 653-672
    • Crandall, M.G.1    Wang, P.-Y.2
  • 12
    • 0348034313 scopus 로고
    • Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations
    • DiBenedetto, E.: Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations. Arch. Rational Mech. Anal. 100(2), 129-147 (1988)
    • (1988) Arch. Rational Mech. Anal. , vol.100 , Issue.2 , pp. 129-147
    • DiBenedetto, E.1
  • 14
    • 0003379820 scopus 로고    scopus 로고
    • Estimates for smooth absolutely minimizing Lipschitz extensions
    • electronic only
    • Evans, L.C.: Estimates for smooth absolutely minimizing Lipschitz extensions. Electron. J. Differential Equations 1993, No. 03, 9 pp. (electronic only)
    • Electron. J. Differential Equations 1993 , Issue.3
    • Evans, L.C.1
  • 15
    • 0032622583 scopus 로고    scopus 로고
    • Differential equations methods for the monge-kantorovich mass transfer problem
    • Evans, L.C., Gangbo, W.: Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Memoirs of the Amer. Math. Soc. 137(653), 1-66 (1999)
    • (1999) Memoirs of the Amer. Math. Soc. , vol.137 , Issue.653 , pp. 1-66
    • Evans, L.C.1    Gangbo, W.2
  • 16
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature. I
    • Evans, L.C., Spruck, J.: Motion of level sets by mean curvature. I. J. Differential Geom. 33(3), 635-681 (1991)
    • (1991) J. Differential Geom. , vol.33 , Issue.3 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 18
    • 0000357774 scopus 로고
    • Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains
    • Giga, Y., Goto, S., Ishii, H., Sato, M.-H.: Comparison Principle and Convexity Preserving Properties for Singular Degenerate Parabolic Equations on Unbounded Domains. Indiana Univ. Math. J. 40(2), 443-470 (1991)
    • (1991) Indiana Univ. Math. J. , vol.40 , Issue.2 , pp. 443-470
    • Giga, Y.1    Goto, S.2    Ishii, H.3    Sato, M.-H.4
  • 19
    • 84972546686 scopus 로고
    • Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor
    • Ishii, H., Souganidis, P.E.: Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor. Tohoku Math. J. (2), 47, 227-250 (1995)
    • (1995) Tohoku Math. J. (2) , vol.47 , pp. 227-250
    • Ishii, H.1    Souganidis, P.E.2
  • 20
    • 0013035240 scopus 로고    scopus 로고
    • Degenerate parabolic PDEs with discontinuities and generalized evolution of surfaces
    • Ishii, H.: Degenerate parabolic PDEs with discontinuities and generalized evolution of surfaces. Adv. Diff. Equations 1(1), 51-72 (1996)
    • (1996) Adv. Diff. Equations , vol.1 , Issue.1 , pp. 51-72
    • Ishii, H.1
  • 21
    • 21144476154 scopus 로고
    • Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
    • Jensen, R.: Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient. Arch. Rational Mech. Anal. 123(1), 51-74 (1993)
    • (1993) Arch. Rational Mech. Anal. , vol.123 , Issue.1 , pp. 51-74
    • Jensen, R.1
  • 22
    • 0036345277 scopus 로고    scopus 로고
    • On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation
    • Juutinen, P., Lindqvist, P., Manfredi, J.: On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation. SIAM J. Math. Anal. 33(3), 699-717 (2001)
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.3 , pp. 699-717
    • Juutinen, P.1    Lindqvist, P.2    Manfredi, J.3
  • 23
    • 18944371166 scopus 로고    scopus 로고
    • Comparison principle and Lipschitz regularity for viscosity solutions of same classes of nonlinear partial differential equations
    • Kawohl, B., Kutev, N.: Comparison principle and Lipschitz regularity for viscosity solutions of same classes of nonlinear partial differential equations, Funkcialaj Ekvacioj 43(2), 241-253 (2000)
    • (2000) Funkcialaj Ekvacioj , vol.43 , Issue.2 , pp. 241-253
    • Kawohl, B.1    Kutev, N.2
  • 24
    • 0009321268 scopus 로고
    • A property of the solutions of parabolic equations with measurable coefficients
    • Krylov, N.V., Safonov, M.V.: A property of the solutions of parabolic equations with measurable coefficients. Izv. Akad. Nauk SSSR Ser. Mat. 44(1), 161-175, 239 (1980)
    • (1980) Izv. Akad. Nauk SSSR Ser. Mat. , vol.44 , Issue.1 , pp. 161-175
    • Krylov, N.V.1    Safonov, M.V.2
  • 26
    • 28244450300 scopus 로고    scopus 로고
    • Another way to say subsolution: The maximum principle and sums of Green functions
    • Laugesen, R., Watson, N.: Another way to say subsolution: the maximum principle and sums of Green functions. Math. Scand. 97(1), 127-153 (2005)
    • (2005) Math. Scand. , vol.97 , Issue.1 , pp. 127-153
    • Laugesen, R.1    Watson, N.2
  • 27
    • 0000130437 scopus 로고    scopus 로고
    • Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation
    • Ohnuma, M., Sato, K.: Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation. Comm. Partial Differential Equations 22(3-4), 381-411 (1997)
    • (1997) Comm. Partial Differential Equations , vol.22 , Issue.3-4 , pp. 381-411
    • Ohnuma, M.1    Sato, K.2
  • 30
    • 18844400607 scopus 로고    scopus 로고
    • 1 regularity for infinity harmonic functions in two dimensions
    • 1 regularity for infinity harmonic functions in two dimensions. Arch. Rational Mech. Anal. 176(3), 351-361 (2005)
    • (2005) Arch. Rational Mech. Anal. , vol.176 , Issue.3 , pp. 351-361
    • Savin, O.1
  • 31
    • 0001409717 scopus 로고
    • A uniqueness theorem for the heat equation
    • Russian
    • Tlhonov, A.N.: A uniqueness theorem for the heat equation. (Russian) Mat. Sb. 2, 199-216 (1935)
    • (1935) Mat. Sb. , vol.2 , pp. 199-216
    • Tlhonov, A.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.