Optimal Concavity for Newtonian Potentials

Concavità ottimale per potenziali newtoniani

Dipartimento di Matematica, Università di Bologna 2018-05-31

In this note I give a short overview about convexity properties of solutions to elliptic equations in convex domains and convex rings and show a result about the optimal concavity of the Newtonian potential of a bounded convex domain in ℝn , n ≥ 3, namely: if the Newtonian potential of a bounded domain is ”sufficiently concave”, then the domain is necessarily a ball. This result can be considered an unconventional overdetermined problem.This paper is based on a talk given by the author in Bologna at the ”Bruno Pini Mathematical Analysis Seminar”, which in turn was based on the paper P. Salani, A characterization of balls through optimal concavity for potential functions, Proc. AMS 143 (1) (2015), 173-183.

Potential theory; Newtonian potential; convexity; geometric properties of solutions; overdetermined problem; 35N25; 35R25; 35R30; 35B06; 52A40; info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion

Open access content. Open access content
Copyright (c) 2017 Paolo Salani

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Bruno Pini Mathematical Analysis Seminar; Seminars 2017; 26-42
English

ITUDB oai:journals.unibo.it:article/7795
https://mathematicalanalysis.unibo.it/article/view/7795
10.6092/issn.2240-2829/7795
1365943492

UNIVERSITA DI BOLOGNA
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