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

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 Lp's theory with 1<p<∞. This paper extends the studies done in [C. Amrouche, V. Girault, J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator, an approach in weighted Sobolev spaces, J. Math. Pures Appl. 76 (1) (1997) 55-81] with Dirichlet and Neumann conditions.