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On the Laplace operator and on the vector potential problems in the half-space: an approach using weighted spaces

✍ Scribed by Tahar Zamène Boulmezaoud

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 297 KB
Volume: 26
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.369

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✦ Synopsis

Abstract

The purpose of the present paper is twofold. The first object is to study the Laplace equation with inhomogeneous Dirichlet and Neumann boundary conditions in the half‐space of ℝ^N^. The behaviour of solutions at infinity is described by means of a family of weighted Sobolev spaces. A class of existence, uniqueness and regularity results are obtained. The second purpose is to investigate some properties of grad, div and curl operators in order to treat curl–div systems of the form

curl w = u, div w = 0

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