We extend an inequality for harmonic functions, obtained by the same authors, to the case of solutions of uniformly elliptic equations in divergence form, with merely measurable coefficients. The inequality for harmonic functions turned out to be a crucial ingredient in the study of the stability of the radial symmetry for Alexandrov’s Soap Bubble Theorem and Serrin’s problem. The proof of our inequality is based on a mean value property for elliptic operators stated and proved in two papers by L. A. Caffarelli and by I. Blank and Z.Hao..

An interpolating inequality for solutions of uniformly elliptic equations / Rolando Magnanini; Giorgio Poggesi. - STAMPA. - (2021), pp. 233-245. [10.1007/978-3-030-73363-6_11]

An interpolating inequality for solutions of uniformly elliptic equations

Rolando Magnanini
;
Giorgio Poggesi
2021

Abstract

We extend an inequality for harmonic functions, obtained by the same authors, to the case of solutions of uniformly elliptic equations in divergence form, with merely measurable coefficients. The inequality for harmonic functions turned out to be a crucial ingredient in the study of the stability of the radial symmetry for Alexandrov’s Soap Bubble Theorem and Serrin’s problem. The proof of our inequality is based on a mean value property for elliptic operators stated and proved in two papers by L. A. Caffarelli and by I. Blank and Z.Hao..
2021
978-3-030-73362-9
Geometric Properties for Parabolic and Elliptic PDE's
233
245
Goal 17: Partnerships for the goals
Rolando Magnanini; Giorgio Poggesi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1211433
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