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Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron
Author(s) -
Petersdorff T. V.,
Stephan E. P.
Publication year - 1990
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.19901490106
Subject(s) - mathematics , gravitational singularity , remainder , mathematical analysis , sobolev space , polyhedron , singularity , pure mathematics , tensor (intrinsic definition) , geometry , arithmetic
The solution of the three‐dimensional Dirichlet problem for the Laplacian in a polyhedral domain has Special singular forms at corners and edges. The main result of this paper is a “tensor‐product” decomposition of those singular forms along the edges. Such a decomposition with both edge singularities, additional corner singularities and a smoother remainder refines known regularity results for the solution where either the edge singularities are of non‐tensor product form or the remainder term belongs to an anisotropic Sobolev space for data given in an isotropic Sobolev space.