JournalsjemsVol. 8 , No. 1DOI 10.4171/jems/41

A symmetry problem in the calculus of variations

  • Graziano Crasta

    Università di Roma La Sapienza, Italy
A symmetry problem in the calculus of variations cover

Abstract

We consider a class of integral functionals defined in a Sobolev space of functions vanishing at the boundary of a nonempty bounded connected open n-dimensional set. We prove that, if the functional admits a minimizer depending only on the distance from the boundary, then that set must be a ball.