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Weighted Sobolev spaces for the Laplace equation in the half-space. (Espaces de Sobolev avec poids pour l’équation de Laplace dans le demi-espace.) (French. Abridged English version) Zbl 0924.35033
Summary: We deal in this note with the Laplace equation in the half-space. The use of a special family of weighted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet and Neumann problems.

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B40 Asymptotic behavior of solutions to PDEs
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