Geodesic
Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 265-274.

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We deal with the Laplace equation in the half space. The use of a special family of weigted 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 problem.
DOI : 10.21136/MB.2001.134013
Classification : 35A05, 35B65, 35J05, 35J25, 58J10
Keywords: the Laplace equation; weighted Sobolev spaces; the half space; existence; uniqueness; regularity 
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     title = {Laplace equation in the half-space with a~nonhomogeneous {Dirichlet} boundary condition},
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Amrouche, Cherif; Nečasová, Šárka. Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition. Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 265-274. doi : 10.21136/MB.2001.134013. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134013/

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