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

Hitoshi Ishii, Moto Hiko Sato

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1077-1098
    Number of pages22
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume57
    Issue number7-8
    DOIs
    Publication statusPublished - 2004 Jun

    Keywords

    • Capillary problem
    • Mean curvature flow
    • Neumann-type boundary conditions
    • Singular degenerate parabolic equations
    • Viscosity solutions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Mathematics(all)

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