16 jan 2013 -- 17:00 [open in google calendar]
Sala Seminari, Department of Mathematics, Pisa University
We consider minimizers of elliptic functionals satisfying homogeneous Dirichlet boundary conditions. We prove that if the minimizer has a level surface which is parallel to boundary, then it must be spherically symmetric. We then extend such result to positive solutions of a wide class of elliptic equations. A particular attention will be devoted to minimizers of non-differentiable functionals and to positive solutions of very degenerate elliptic equations, which are equations whose ellipticity constants degenerate at every point where the gradient belongs to some nontrivial convex set.