In 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.
Symmetry and asymmetry of minimizers of a class of noncoercive functionals / Friedemann, Brock; Gisella, Croce; Olivier, Guibé; Mercaldo, Anna. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - 13:1(2020), pp. 15-32. [10.1515/acv-2017-0005]
Symmetry and asymmetry of minimizers of a class of noncoercive functionals
MERCALDO, ANNA
2020
Abstract
In 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.