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Dirichlet Problems in Polyhedral Domains I: Regularity of the Solutions

✍ Scribed by Jean Mbaro-Saman Lubuma; Serge Nicaise

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
771 KB
Volume
168
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The solution of the Dirichlet problem relative to an elliptic operator in a polyhedron has a complex singular behaviour near edges and vertices. Here we show that this solution and its conormal derivative have a global regularity in appropriate weighted Sobolev spaces. We also investigate some compact embeddings of these spaces. The present results will be applied in a forthcoming work to the constructive treatment of the problem by optimal convergent finite clement method and boundary element method.

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