The infuence of domain geometry in the boundary behavior of large solutions of degenerate elliptic problems

Michèle Grillot (1) , Philippe Grillot (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper we study the asymptotic boundary behavior of large solutions of the equation Delta u = d^{alpha} u^p in a regular bounded domain Omega in R^N, N >= 2, where d(x) denotes the distance from x to d Omega, p > 1 and alpha > 0. We precise the expansion which depends on the mean curvature of the boundary.

Mots clés: elliptic equations; boundary behavior; blow-up

Domaines: Equations aux dérivées partielles [math.AP]

Michèle Grillot, Philippe Grillot. The infuence of domain geometry in the boundary behavior of large solutions of degenerate elliptic problems. Port. Math. (N.S.), 2007, 64 (2), pp.143-153. ⟨hal-00112159⟩