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arXiv · 1708.07392

Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities

Rolando Magnanini·Giorgio Poggesi
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Abstract

We consider Serrin's overdetermined problem for the torsional rigidity and Alexandrov's Soap Bubble Theorem. We present new integral identities, that show a strong analogy between the two problems and help to obtain better (in some cases optimal) quantitative estimates for the radially symmetric configuration. The estimates for the Soap Bubble Theorem benefit from those of Serrin's problem.

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Rolando Magnanini, Giorgio Poggesi. 2017-08-24. Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities. https://arxiv.org/abs/1708.07392

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