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.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2004 6月|
ASJC Scopus subject areas
- 数学 (全般)