The $p$-Laplacian overdetermined problem on Riemannian manifolds

Fan Chen; Qihua Ruan; Qin Huang

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The p-Laplacian overdetermined problem on Riemannian manifolds

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arxiv 2305.03492 v1 pith:ZMRYV2FG submitted 2023-05-05 math.AP

The $p$-Laplacian overdetermined problem on Riemannian manifolds

Qihua Ruan , Qin Huang , Fan Chen This is my paper

classification math.AP

keywords laplacianoverdeterminedproblemequationmanifoldsobtainresultsriemannian

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abstract

In this paper, we study the overdetermined problem for the $p$-Laplacian equation on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. We prove that the regularity results of weak solutions of the $p$-Laplacian equation and obtain some integral identities. As their applications, we give the proof of the $p$-Laplacian overdetermined problem and obtain some well known results such as the Heintze-Karcher inequality and the Soap Bubble Theorem.

The $p$-Laplacian overdetermined problem on Riemannian manifolds

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