Équations aux dérivées partielles
Symétrie des grandes solutions d'équations elliptiques semi linéaires
[Symmetry of large solutions of semilinear elliptic equations]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 483-487.

Let g be a locally Lipschitz continuous function defined on R. We assume that g satisfies the Keller–Osserman condition and there exists a positive real number a such that g is convex on [a,). Then any solution u of Δu+g(u)=0 in a ball B of RN, N2, which tends to infinity on ∂B, is spherically symmetric.

Soit g une fonction localement lipschitzienne de la variable réelle. On suppose que g vérifie la condition de Keller et Osserman et qu'il existe un réel a>0 tel que g est convexe sur [a,+[. Alors toute solution u de Δu+g(u)=0 dans une boule B de RN, N2, qui tend vers l'infini au bord de B, est une fonction radiale.

Received:
Published online:
DOI: 10.1016/j.crma.2006.01.020
Porretta, Alessio 1; Véron, Laurent 2

1 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italie
2 Laboratoire de mathématiques et physique théorique, CNRS UMR 6083, faculté des sciences, 37200 Tours, France
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Porretta, Alessio; Véron, Laurent. Symétrie des grandes solutions d'équations elliptiques semi linéaires. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 483-487. doi : 10.1016/j.crma.2006.01.020. http://www.numdam.org/articles/10.1016/j.crma.2006.01.020/

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