MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 265-274 (2001)

Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition

Cherif Amrouche, Sarka Necasova

Cherif Amrouche, Universite de Pau et des Pays de L'Adour, Laboratoire de Mathematiques Appliquees, I.P.R.A, Av. de l'Universite, 6400 Pau, France, e-mail: cherif.amrouche@univ-pau.fr; Sarka Necasova, Mathematical Institute of the Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: matus@math.cas.cz

Abstract: 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.

Keywords: the Laplace equation, weighted Sobolev spaces, the half space, existence, uniqueness, regularity

Classification (MSC2000): 35J05, 58J10

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