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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.

MSC:
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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