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The Laplace and the linear elasticity problems near polyhedral corners and associated eigenvalue problems

✍ Scribed by Arnd Meyer; Cornelia Pester

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
250 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

For domains with concave corners, the solutions to elliptic boundary values have the typical r^Ξ±^‐singularity. The so‐called singularity exponents Ξ± are the eigenvalues of an eigenvalue problem which is associated with the given boundary value problem. This paper is aimed at deriving the mentioned eigenvalue problems for two examples, the Laplace equation and the linear elasticity problem.

We will show interesting properties of these eigenvalue problems. For the linear elasticity problem, we explain in addition why the classical symmetry and positivity assumptions of the material tensor have to be used with care. Copyright Β© 2006 John Wiley & Sons, Ltd.

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