a local symmetry result for linear elliptic problems with solutions changing sign

BRUNO CANUTO

ANNALES DE L4INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

GAUTHIER-VILLARS/EDITIONS ELSEVIER

Año: 2011 p. 551 - 564

0294-1449

oindent {it Abstract}{f quad }We prove that the only domain $Omega $such that there exists a solution to the following problem $Delta u+omega^2u=-1$ in $Omega $, $u=0$ on $partial Omega $, and $ rac 1{left|partial Omega ight| }intlimits_{partial Omega }partial _{{f n}%}u=c $, for a given constant $c$, is the unit ball $B_1$, if we assume that $%Omega $ lies in a appropriate class of Lipschitz domains.