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.
Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities / Rolando Magnanini, Giorgio Poggesi. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 69:(2020), pp. 1181-1205. [10.1512/iumj.2020.69.7925]
Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities
Rolando Magnanini
;Giorgio Poggesi
2020
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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MagnaniniPoggesiArx1708.07392v2.pdf
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