Symmetry of large solutions of nonlinear elliptic equations in a ball

Alessio Porretta (1) , Laurent Veron (2)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

Let $g$ be a locally Lipschitz continuous real valued function which satisfies the Keller-Osserman condition and is convex at infinity, then any large solution of $-\Delta u+g(u)=0$ in a ball is radially symmetric.

Mots clés: Elliptic equations; Boundary blow-up; Keller–Osserman condition; Radial symmetry; Spherical Laplacian

Domaines: Equations aux dérivées partielles [math.AP]

Alessio Porretta, Laurent Veron. Symmetry of large solutions of nonlinear elliptic equations in a ball. J Funct Analysis, 2006, 236, pp.581-591. ⟨10.1016/j.jfa.2006.03.010⟩. ⟨hal-00280029⟩