Symmetry properties for the extremals of the Sobolev trace embedding

JULIAN FERNANDEZ BONDER; ENRIQUE LAMI-DOZO; ROSSI, JULIO DANIEL

ANNALES DE L4INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

GAUTHIER-VILLARS/EDITIONS ELSEVIER

Año: 2004 p. 795 - 805

0294-1449

In this article we study symmetry properties ofthe extremals for the Sobolev trace embedding$H^1 (B(0,mu)) hookrightarrow L^q (partial B(0,mu))$ with$1le qle 2(N-1)/(N-2)$ for different values of $mu$.These extremals $u$ are solutions of the problem$$left{egin{array}{ll} Delta u  = u  qquad & mbox{in } B(0,mu),rac{partial u}{partial eta}  = lambda |u|^{q-2} u qquad & mbox{on }partial B(0,mu).end{array} ight.$$We find that, for $1le q