Existence and symmetry of minimizers for nonconvex radially symmetric variational problems

We study functionals of the form where u is a real valued function over the ball which vanishes on the boundary and W is nonconvex. The functional is assumed to be radially symmetric in the sense that W only depends on . Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation. Our assumptions on G do not include convexity, thus extending a result of A. Cellina and S. Perrotta.