Asymptotics of the eigenvalues of the Dirichlet-Laplace problem in a domain with thin tube excluded

Author:
X. Claeys

Journal:
Quart. Appl. Math. **74** (2016), 595-605

MSC (2010):
Primary 35B25

DOI:
https://doi.org/10.1090/qam/1436

Published electronically:
June 17, 2016

MathSciNet review:
3539023

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a Laplace problem with Dirichlet boundary condition in a three dimensional domain containing an inclusion taking the form of a thin tube with small thickness . We prove convergence in operator norm of the resolvent of this problem as , establishing that the perturbation induced by the inclusion on the resolvent is not greater than for some . We deduce convergence of the eigenvalues of the perturbed operator toward the limit operator.

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Additional Information

**X. Claeys**

Affiliation:
Laboratoire Jacques-Louis Lions, UPMC University of Paris 6 and CNRS UMR 7598, 75005, Paris, France;;
INRIA-Paris-Rocquencourt, EPC Alpines, Le Chesnay Cedex, France

Email:
claeys@ann.jussieu.fr

DOI:
https://doi.org/10.1090/qam/1436

Received by editor(s):
February 25, 2015

Published electronically:
June 17, 2016

Article copyright:
© Copyright 2016
Brown University