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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Acknowledgements
The third author would like to thank Professor Jianqing Chen in Fujian Normal University for his careful guidance. And the authors would also like to thank anonymous reviewers for their valuable comments and suggestions, which improves the original manuscripts.
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This work was supported by NSF of China (No. 11971253) and NSF of Fujian Province (No. 2021J011101).
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Ruan, Q., Huang, Q. & Chen, F. The p-Laplacian overdetermined problem on Riemannian manifolds. Annali di Matematica 203, 647–662 (2024). https://doi.org/10.1007/s10231-023-01377-0
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DOI: https://doi.org/10.1007/s10231-023-01377-0