Uniqueness for an overdetermined boundary value problem for the p-Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Uniqueness for an overdetermined boundary value problem for the p-Laplacian

Authors:	Farid Bahrami Henrik Shahgholian

Institution:	Department of Mathematics, University of Tehran, P.O. Box 13145-1873, Tehran, Iran Henrik Shahgholian ; Department of Mathematics, The Royal Institute of Technology, 100 44 Stockholm, Sweden

Abstract:	For set $\Delta _p u = {\mathrm{div}}(\|\nabla u\|^{p-2}\nabla u)$ , and let $\mu$ be a measure with compact support. Suppose, for , there are functions $u_j \in W^{1,p}$ and (bounded) domains $\Omega _j$ , both containing the support of $\mu$ with the property that $\Delta _p u_j =\chi _{\Omega _j} - \mu$ in $\mathbf{R}^N$ (weakly) and in the complement of $\Omega _j$ . If in addition $\Omega _1 \cap \Omega _2$ is convex, then $\Omega _1 \equiv \Omega _2$ and $u_1\equiv u_2$ .

Keywords:	Inverse domain problem p-Laplacian uniqueness

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