Symmetry of large solutions of semilinear elliptic equations [Symétrie des grandes solutions d'équations elliptiques semi linéaires]

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.