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Some Sphere Theorems In Linear Potential Theory
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, PI, Italy;Univ Trento, Via Sommar 14, I-38123 Povo, TN, Italy.ORCID iD: 0000-0002-6505-5876
Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, PI, Italy;Univ Libre Bruxelles, Dept Math, Ave Franklin Roosevelt 50, B-1050 Brussels, Belgium.
Univ Trento, Via Sommar 14, I-38123 Povo, TN, Italy.
2019 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 371, no 11, p. 7757-7790Article in journal (Refereed) Published
Abstract [en]

In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular bounded domain Omega subset of R-n, n >= 3, we prove that if the mean curvature H of the boundary obeys the condition -[1/Cap(Omega)](1/n-2) <= H/n-1 <= [1/Cap(Omega)](1/n-2), then Omega is a round ball.

Place, publisher, year, edition, pages
AMER MATHEMATICAL SOC , 2019. Vol. 371, no 11, p. 7757-7790
Keywords [en]
Capacity, electrostatic potential, overdetermined boundary value problems
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-386438DOI: 10.1090/tran/7637ISI: 000469491900010OAI: oai:DiVA.org:uu-386438DiVA, id: diva2:1331083
Available from: 2019-06-26 Created: 2019-06-26 Last updated: 2019-06-26Bibliographically approved

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Borghini, Stefano

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