Symmetry results for some overdetermined obstacle problems

Nicola De Nitti; Shigeru Sakaguchi

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arXiv · 2306.12124

Symmetry results for some overdetermined obstacle problems

Nicola De Nitti·Shigeru Sakaguchi

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Abstract

We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the method of moving planes; instead, it leverages the comparison principle and the fact that the solution of the obstacle problem is superharmonic within its domain. The second proof utilizes a suitable version of Serrin's method of moving planes.

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Nicola De Nitti, Shigeru Sakaguchi. 2023-06-21. Symmetry results for some overdetermined obstacle problems. https://arxiv.org/abs/2306.12124

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