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Nearly optimal stability for Serrin’s problem and the Soap Bubble theorem

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Abstract

We present new quantitative estimates for the radially symmetric configuration concerning Serrin’s overdetermined problem for the torsional rigidity, Alexandrov’s Soap Bubble theorem, and other related problems. The new estimates improve on those obtained in Magnanini and Poggesi (J Anal Math, 139(1), 179–205, 2019), Magnanini and Poggesi (Indiana Univ Math J, arXiv:1708.07392, 2017) and are in some cases optimal.

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Acknowledgements

The authors wish to thank the anonymous referee, who hinted the estimate (2.21) and whose suggestions contributed to a better presentation of this article. The paper was partially supported by the Gruppo Nazionale Analisi Matematica Probabilità e Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Authors and Affiliations

  1. Dipartimento di Matematica ed Informatica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134, Florence, Italy

    Rolando Magnanini

  2. Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA, 6009, Australia

    Giorgio Poggesi

Authors
  1. Rolando Magnanini
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  2. Giorgio Poggesi
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Correspondence to Giorgio Poggesi.

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Communicated by J. Jost.

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Magnanini, R., Poggesi, G. Nearly optimal stability for Serrin’s problem and the Soap Bubble theorem. Calc. Var. 59, 35 (2020). https://doi.org/10.1007/s00526-019-1689-7

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