Let g be a locally Lipschitz continuous function defined on ℠. We assume that g satisfies the Keller-Osserman condtion 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 ℠N, N ≥ 2, which tends to infinity on ∂ B, is spherically symmetric. © 2006 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.
Porretta, A., Veron, L. (2006). Symmetry of large solutions of semilinear elliptic equations [Symétrie des grandes solutions d'équations elliptiques semi linéaires]. COMPTES RENDUS MATHÉMATIQUE, 342(7), 483-487 [10.1016/j.crma.2006.01.020].
Symmetry of large solutions of semilinear elliptic equations [Symétrie des grandes solutions d'équations elliptiques semi linéaires]
PORRETTA, ALESSIO;
2006-01-01
Abstract
Let g be a locally Lipschitz continuous function defined on ℠. We assume that g satisfies the Keller-Osserman condtion 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 ℠N, N ≥ 2, which tends to infinity on ∂ B, is spherically symmetric. © 2006 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
