In this paper we study the problem of the axial symmetry of solutions of some semilinear elliptic equations in unbounded domains. Assuming that the solutions have Morse index one and that the nonlinearity is strictly convex in the second variable, we are able to prove several symmetry results in R-n and in the exterior of a ball. The case of some bounded domains is also discussed.
Axial symmetry of solutions to semilinear elliptic equations in unbounded domains / Montefusco, Eugenio. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 133:5(2003), pp. 1175-1192. [10.1017/s0308210500002869]
Axial symmetry of solutions to semilinear elliptic equations in unbounded domains
MONTEFUSCO, Eugenio
2003
Abstract
In this paper we study the problem of the axial symmetry of solutions of some semilinear elliptic equations in unbounded domains. Assuming that the solutions have Morse index one and that the nonlinearity is strictly convex in the second variable, we are able to prove several symmetry results in R-n and in the exterior of a ball. The case of some bounded domains is also discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
