The $p$-Laplacian overdetermined problem on Riemannian manifolds

Qihua Ruan; Qin Huang; Fan Chen

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arXiv · 2305.03492

The $p$-Laplacian overdetermined problem on Riemannian manifolds

Qihua Ruan·Qin Huang·Fan Chen

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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.

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Qihua Ruan, Qin Huang, Fan Chen. 2023-05-05. The $p$-Laplacian overdetermined problem on Riemannian manifolds. https://arxiv.org/abs/2305.03492

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