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Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition. (English) Zbl 0979.35038
Summary: We deal 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 the inhomogeneous Dirichlet problem.

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
58J10 Differential complexes
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