论文信息 - Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

Abstract We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.

Hitoshi Ishii | H. Ishii | Moto-Hiko Sato | Moto Hiko Sato

[1] Yun-Gang Chen,et al. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations , 1989 .

[2] H. Ishii. Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s , 1991 .

[3] J. Carifio,et al. Nonlinear Analysis , 1995 .

[4] L. Evans,et al. Motion of level sets by mean curvature. II , 1992 .

[5] G. Barles. Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications , 1999 .

[6] Hitoshi Ishii,et al. Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor , 1995 .

[7] Moto-Hiko Sato,et al. Stability of stationary interfaces with contact angle in a generalized mean curvature flow , 1996 .

[8] G. Barles. Fully non-linear Neumann type boundary conditions for second-order elliptic and parabolic equations , 1993 .

[9] Yoshikazu Giga,et al. Neumann problem for singular degenerate parabolic equations , 1992, Differential and Integral Equations.

[10] P. Lyons. Neumann Type Boundary Conditions for Hamilton-Jacobi Equations. , 1985 .

[11] P. Lions,et al. User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[12] Moto-Hiko Sato. Interface evolution with Neumann boundary condition , 1992 .