메뉴 건너뛰기




Volumn 33, Issue 3, 1991, Pages 749-786

Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84972499852     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214446564     Document Type: Article
Times cited : (798)

References (26)
  • 1
    • 84972511388 scopus 로고
    • The normalized curve shortening flow and homothetic solutions
    • U. Abresch & J. Langer, The normalized curve shortening flow and homothetic solutions, J. Differential Geometry 23 (1986) 175-196.
    • (1986) J. Differential Geometry , vol.23 , pp. 175-196
    • Abresch, U.1    Langer, J.2
  • 2
    • 0002867833 scopus 로고
    • Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it
    • (Russian)
    • A. D. Alexandroff, Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it, Leningrad Gos. Univ. Uchen. Zap. Ser. Mat. Nauk 6 (1939) 3-35. (Russian)
    • (1939) Leningrad Gos. Univ. Uchen. Zap. Ser. Mat. Nauk , vol.6 , pp. 3-35
    • Alexandroff, A.D.1
  • 5
    • 0142077747 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y. -G. Chen, Y. Giga & S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Proc. Japan Acad. Ser. A 65 (1989) 207-210.
    • (1989) Proc. Japan Acad. Ser. A , vol.65 , pp. 207-210
    • Chen, Y.-G.1    Giga, Y.2    Goto, S.3
  • 6
    • 84974000612 scopus 로고
    • Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order
    • M. G. Crandall, Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order, Ann. Inst. H. Poincaré Anal. Non Linéare 6 (1989) 419-435.
    • (1989) Ann. Inst. H. Poincaré Anal. Non Linéare , vol.6 , pp. 419-435
    • Crandall, M.G.1
  • 8
    • 84990574955 scopus 로고
    • A stable manifold theorem for the curve shortening equation
    • C. Epstein & M. Weinstein, A stable manifold theorem for the curve shortening equation, Comm. Pure Appl. Math. 40 (1987) 119-139.
    • (1987) Comm. Pure Appl. Math , vol.40 , pp. 119-139
    • Epstein, C.1    Weinstein, M.2
  • 10
    • 84963023423 scopus 로고
    • The heat equation shrinking of convex plane curves
    • M. Gage & R. Hamilton, The heat equation shrinking of convex plane curves, J. Differential Geometry 23 (1986) 69-96.
    • (1986) J. Differential Geometry , vol.23 , pp. 69-96
    • Gage, M.1    Hamilton, R.2
  • 11
    • 0002179973 scopus 로고
    • Convergence problems for functionals and operators
    • (E. De Georgi et al., eds.), Pitagora Editrice, Bologna
    • E. De Giorgi, Convergence problems for functionals and operators, Proc. Internat. Meeting on Recent Methods in Nonlinear Analysis (E. De Georgi et al., eds.), Pitagora Editrice, Bologna, 1979, 131-188.
    • (1979) Proc. Internat. Meeting on Recent Methods in Nonlinear Analysis , pp. 131-188
    • De Giorgi, E.1
  • 12
    • 84972528479 scopus 로고
    • The heat equation shrinks embedded plane curves to round points
    • M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geometry 26 (1987) 285-314.
    • (1987) J. Differential Geometry , vol.26 , pp. 285-314
    • Grayson, M.1
  • 13
    • 0001448409 scopus 로고
    • Towards a nonequilibrium thermodynamics of two-phase materials
    • M. Gurtin, Towards a nonequilibrium thermodynamics of two-phase materials, Arch. Rational Mech. Anal. 100 (1988) 275-312.
    • (1988) Arch. Rational Mech. Anal , vol.100 , pp. 275-312
    • Gurtin, M.1
  • 14
    • 84972507688 scopus 로고
    • Flow by mean curvature of convex surfaces into spheres
    • G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geometry 20 (1984) 237-266.
    • (1984) J. Differential Geometry , vol.20 , pp. 237-266
    • Huisken, G.1
  • 15
    • 84972527004 scopus 로고
    • Asymptotic behavior for singularities of the mean curvature flow
    • G. Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geometry 31 (1990) 285-299.
    • (1990) J. Differential Geometry , vol.31 , pp. 285-299
    • Huisken, G.1
  • 16
    • 84972566521 scopus 로고
    • Perron's method for Hamilton-Jacobi equations
    • H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987) 369- 384.
    • (1987) Duke Math. J , vol.55 , pp. 369-384
    • Ishii, H.1
  • 17
    • 84990575194 scopus 로고
    • On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's
    • H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's, Comm. Pure Appl. Math. 42 (1989) 15-45.
    • (1989) Comm. Pure Appl. Math , vol.42 , pp. 15-45
    • Ishii, H.1
  • 18
    • 0002824461 scopus 로고
    • Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
    • H. Ishii & P. L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990) 26-78.
    • (1990) J. Differential Equations , vol.83 , pp. 26-78
    • Ishii, H.1    Lions, P.L.2
  • 19
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second-order partial differential equations
    • R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second-order partial differential equations, Arch. Rational Mech. Anal. 101 (1988) 1-27.
    • (1988) Arch. Rational Mech. Anal , vol.101 , pp. 1-27
    • Jensen, R.1
  • 20
    • 84966259849 scopus 로고
    • A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations
    • R. Jensen, P. L. Lions & P. E. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations, Proc. Amer. Math. Soc. 102 (1988) 975-978.
    • (1988) Proc. Amer. Math. Soc , vol.102 , pp. 975-978
    • Jensen, R.1    Lions, P.L.2    Souganidis, P.E.3
  • 21
    • 51249173208 scopus 로고
    • A remark on regularization in Hilbert spaces
    • J. M. Lasry & P. L. Lions, A remark on regularization in Hilbert spaces, Israel J. Math. 55 (1986) 257-266.
    • (1986) Israel J. Math , vol.55 , pp. 257-266
    • Lasry, J.M.1    Lions, P.L.2
  • 22
    • 84953017099 scopus 로고
    • Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part II: Viscosity solutions and uniqueness
    • P. L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part II: Viscosity solutions and uniqueness, Comm. Partial Differential Equations 8 (1983) 1229-1276.
    • (1983) Comm. Partial Differential Equations , vol.8 , pp. 1229-1276
    • Lions, P.L.1
  • 24
    • 84972519729 scopus 로고
    • Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with noncontinuous time-dependence
    • D. Nunziante, Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with noncontinuous time-dependence, Differential Integral Equations 3 (1990) 77-91.
    • (1990) Differential Integral Equations , vol.3 , pp. 77-91
    • Nunziante, D.1
  • 25
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher & J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Computational Phys. 79 (1988) 12-49.
    • (1988) J. Computational Phys , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 26
    • 84972535294 scopus 로고
    • Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws
    • J. A. Sethian, Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws, J. Differential Geometry 31 (1990) 131-161.
    • (1990) J. Differential Geometry , vol.31 , pp. 131-161
    • Sethian, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.