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arXiv · 2005.04797

Existence and Symmetry results for some overdetermined free boundary problems

Mohammed Barkatou
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Abstract

In this paper, we prove that a domain which verifies some integral inequality is either (strictly) contained in the solution of some free boundary problem, or it coincides with an $N$-ball. We also present new overdetermined value problems which have an $N$-ball as a solution. To reach our results, we use an integral identity which involves the domain derivative of the solution of Dirichlet problem.

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Mohammed Barkatou. 2020-05-10. Existence and Symmetry results for some overdetermined free boundary problems. https://arxiv.org/abs/2005.04797

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