ON THE BEHAVIOUR OF THE SOLUTIONS TO p-LAPLACIAN EQUATIONS

Abstract

− div ( |∇up|p−2∇up ) = f in Ω up = 0 on ∂Ω, where p > 1 and Ω is a bounded open set of R (N ≥ 2) with Lipschitz boundary. We analyze the case where Ω is a ball and the datum f is a non-negative radially decreasing function belonging to the Lorentz space LN,∞(Ω) and the case where the datum f belongs to the dual space W−1,∞(Ω). We are interested in finding the pointwise limit of up as p goes to 1 and in proving that such a limit is a solution to the “limit equation” of (1.1), namely:

Cite this paper

@inproceedings{Mercaldo2008ONTB, title={ON THE BEHAVIOUR OF THE SOLUTIONS TO p-LAPLACIAN EQUATIONS}, author={Anna Mercaldo and Sergio Segura de Le{\'o}n and C. Trombetti}, year={2008} }