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

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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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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  • DOI: https://doi.org/10.1007/s00526-019-1689-7

Mathematics Subject Classification

  • Primary 35N25
  • 53A10
  • 35B35
  • Secondary 35A23