Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems

Abstract

We determine a class of Carathéodory functions G for which the minimum formulated in the problem (1.1) below is achieved at a Schwarz symmetric function satisfying the constraint. Our hypotheses about G seem natural and, as our examples show, they are optimal from some points of view. © Springer-Verlag 2004.