Exterior problems in the half-space for the Laplace operator in weighted Sobolev spaces

Chérif Amrouche (1) , Florian Bonzom (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The purpose of this work is to solve exterior problems in the half-space for the Laplace operator. We give existence and unicity results in weighted $L^p$'s theory with $ 1 < p < \infty$. This paper extends the studies done in \cite{A2} with Dirichlet and Neumann conditions.

Keywords: Weighted Sobolev spaces; Laplacian; Dirichlet and Neumann boundary conditions; Exterior problems; Half-space.; Half-space

Domains: Analysis of PDEs [math.AP]

Chérif Amrouche, Florian Bonzom. Exterior problems in the half-space for the Laplace operator in weighted Sobolev spaces. Journal of Differential Equations, 2009, 246 (5), pp.1894-1920. ⟨10.1016/j.jde.2008.11.021⟩. ⟨hal-00297277⟩