Uniqueness for an overdetermined boundary value problem for the p-Laplacian
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- by Farid Bahrami and Henrik Shahgholian PDF
- Proc. Amer. Math. Soc. 126 (1998), 745-750 Request permission
Abstract:
For $p>1$ set $\Delta _p u = {\mathrm {div}}(|\nabla u|^{p-2}\nabla u)$, and let $\mu$ be a measure with compact support. Suppose, for $j=1,2$, 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 $u_j=0$ in the complement of $\Omega _j$. If in addition $\Omega _1 \cap \Omega _2$ is convex, then $\Omega _1 \equiv \Omega _2$ and $u_1\equiv u_2$.References
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Additional Information
- Farid Bahrami
- Affiliation: Department of Mathematics, University of Tehran, P.O. Box 13145-1873, Tehran, Iran
- Henrik Shahgholian
- Affiliation: Department of Mathematics, The Royal Institute of Technology, 100 44 Stockholm, Sweden
- Email: henriks@math.kth.se
- Received by editor(s): April 3, 1996
- Received by editor(s) in revised form: August 28, 1996
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 745-750
- MSC (1991): Primary 31B20, 35J05, 35R35
- DOI: https://doi.org/10.1090/S0002-9939-98-04087-8
- MathSciNet review: 1422844