Maximum principle for viscosity solutions on Riemannian manifolds

Abstract

In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity version.

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• Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds
• A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
• Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds