Symmetry and asymmetry of minimizers of a class of noncoercive functionals-Reference-Cited by-同舟云学术

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Published:2020-01-01 Issue:1 Volume:13 Page:15-32
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
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Author:

Brock Friedemann¹,Croce Gisella²,Guibé Olivier³,Mercaldo Anna⁴

Affiliation:

1. Institute of Mathematics, University of Rostock, Ulmenstr. 69, Bldg. 3, 18057Rostock, Germany

2. Laboratoire de Mathématiques Appliquées du Havre, Université Le Havre Normandie, ULH, LMAH, FR CNRS 3335, 25 rue Philippe Lebon, 76600Le Havre, France

3. Laboratoire de Mathématiques Raphaël Salem CNRS, Université de Rouen Normandie, Avenue de l’Université, BP. 12, 76801Saint-Étienne du Rouvray, France

4. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126Napoli, Italy

Abstract

AbstractIn this paper we prove symmetry results for minimizers of a noncoercive functional defined on the class of Sobolev functions with zero mean value. We prove that the minimizers are foliated Schwarz symmetric, i.e., they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. In the two-dimensional case, we show a symmetry breaking.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2017-0005/pdf

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