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Dirichlet Problems in Polyhedral Domains I: Regularity of the Solutions
Author(s) -
Lubuma Jean MbaroSaman,
Nicaise Serge
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941680115
Subject(s) - mathematics , polyhedron , constructive , sobolev space , pure mathematics , dirichlet distribution , boundary (topology) , dirichlet problem , domain (mathematical analysis) , mathematical analysis , boundary value problem , geometry , computer science , process (computing) , operating system
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.