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

By Rolando Magnanini, Giorgio Poggesi. Indiana University Mathematics Journal, 2017

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/443c014175df47bba7aa7b06b3835aec2d837dc3