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”.
OPTIMAL CONCAVITY FOR NEWTONIAN POTENTIALS / Salani, P. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - STAMPA. - 1:(2017), pp. 26-42. [10.6092/issn.2240-2829/7795]
OPTIMAL CONCAVITY FOR NEWTONIAN POTENTIALS
Salani, P
2017
Abstract
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”.File | Dimensione | Formato | |
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