Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

Symmetry of minimizers with a level surface parallel to the boundary

Giulio Ciraolo

created by magnani on 10 Jan 2013

16 jan 2013 -- 17:00   [open in google calendar]

Sala Seminari, Department of Mathematics, Pisa University

Abstract.

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.

Credits | Cookie policy | HTML 5 | CSS 2.1