Some remark on solutions to an overdetermined elliptic problem in divergence form in a ball

BRUNO CANUTO, DIEGO RIAL

ANNALI DI MATEMATICA PURA ED APPLICATA

Año: 2007 vol. 186 p. 591 - 602

0373-3114

Summary: "We prove the existence of a continuum of non-radial pair $(k,u)$ solutions to the following overdetermined problem: $${ m div}(k abla u)=-1quad ext{ in} B_r,$$ $$u=0quad ext{ and}quad k abla u·n=-rac rnquad ext{ on} partial B_r,$$ where $B_r$ is the Euclidean ball centered at zero of radius $r$ in $Bbb{R}^n$."