Viscosity solutions of second order partial differential equations with boundary conditions on Riemannian manifolds. (November 2016)

• Record Type: Journal Article
• Authors: Khajehpour, S.; Pouryayevali, M.R.
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 211
• Page End: 232
• Publication Date: 2016-11
• Subjects: Dirichlet boundary condition -- Neumann boundary condition -- Proper second order PDEs -- Riemannian manifold -- Viscosity solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.08.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The comparison, uniqueness and existence for viscosity solution to a class of fully nonlinear second order partial differential equations with boundary condition on a finite dimensional Riemannian manifold are studied. Some results regarding the regularity of the boundary are obtained. These results show that every compact manifold with C 1, 1 boundary satisfies the regularity condition.