Maximum principle for viscosity solutions on Riemannian manifolds

Shige Peng; Detang Zhou

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arXiv · 0806.4768

Maximum principle for viscosity solutions on Riemannian manifolds

Shige Peng·Detang Zhou

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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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Shige Peng, Detang Zhou. 2008-06-29. Maximum principle for viscosity solutions on Riemannian manifolds. https://arxiv.org/abs/0806.4768

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