Two overdetermined problems for anisotropic $ p $-Laplacian

Chao Xia; Jiabin Yin; Chao Xia; Jiabin Yin

doi:10.3934/mine.2022015

Mathematics in Engineering

2022, Volume 4, Issue 2: 1-18. doi: 10.3934/mine.2022015

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Two overdetermined problems for anisotropic $ p $-Laplacian

Chao Xia ^,,
Jiabin Yin ^,

School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

Received: 26 January 2021 Accepted: 23 June 2021 Published: 13 July 2021

In this paper, we consider two overdetermined problems for the anisotropic $ p $-Laplacian ($ 1 < p\leq n $) in the exterior domains and the bounded punctured domains, respectively, and prove the corresponding Wulff shape characterizations, by using Weinberger type approach.
- anisotropic $ p $-Laplacian,
- capacity,
- overdetermined problems,
- Wulff shape
Citation: Chao Xia, Jiabin Yin. Two overdetermined problems for anisotropic $ p $-Laplacian[J]. Mathematics in Engineering, 2022, 4(2): 1-18. doi: 10.3934/mine.2022015

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Abstract

In this paper, we consider two overdetermined problems for the anisotropic $ p $-Laplacian ($ 1 < p\leq n $) in the exterior domains and the bounded punctured domains, respectively, and prove the corresponding Wulff shape characterizations, by using Weinberger type approach.

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