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arXiv · 2005.04921

The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary

Rirong Yuan
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Abstract

This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense that the mean curvature of the boundary is \textit{nonpositive}. The proof is primarily based on a quantitative boundary estimate. Also, we obtain analogous results in complex variables. In Appendix, the subsolutions are also constructed on certain topologically product manifolds.

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Rirong Yuan. 2020-05-11. The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary. https://arxiv.org/abs/2005.04921

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