Symmetry and asymmetry of minimizers of a class of noncoercive functionals (Q2285851)

This paper is mainly concerned with symmetry results for minimizers of noncoercive functionals. A feature of the paper under review is that these functionals are defined on a class of \(L^p\)-normalized Sobolev functions with zero mean value. The authors establish that the minimizers are foliated Schwarz symmetric, in the sense that they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. In the final part of this paper, the authors prove an interesting symmetry breaking phenomenon.