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 two our previous articles, and are in some cases optimal.

20 pages. The present article contains results obtained in the PhD thesis [arXiv:1902.08584] of the second author of which the first author has been the advisor. The article has been accepted by Calculus of Variations and Partial Differential Equations. This amended version incorporates referee's suggestions. A final version is in print