The p-Laplacian overdetermined problem on Riemannian manifolds

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.