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Axial symmetry of solutions to semilinear elliptic equations in unbounded domains

Published online by Cambridge University Press:  12 July 2007

Eugenio Montefusco
Eugenio Montefusco
Affiliation:
Dipartimento di Matematica, Università degli Studi di Roma la Sapienza, Piazzale A. Moro 5, 00185 Roma, Italy
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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 Rn and in the exterior of a ball. The case of some bounded domains is also discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 5 , October 2003 , pp. 1175 - 1192
Copyright
Copyright © Royal Society of Edinburgh 2003

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