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The eigenvalues of the Laplacian on domains with small slits
Author(s):
Luc
Hillairet;
Chris
Judge
Journal:
Trans. Amer. Math. Soc.
362
(2010),
6231-6259.
MSC (2010):
Primary 58C40;
Secondary 58J37, 35P20
Posted:
August 3, 2010
MathSciNet review:
2678972
Retrieve article in:
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Abstract:
We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an eigenvalue of the original domain. By combining this with our earlier work (2009), we obtain the following application: The generic multiply connected polygon has a simple spectrum.
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Additional Information:
Luc
Hillairet
Affiliation:
Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, Université de Nantes, 2 rue de la Houssinière, BP 92 208, F-44 322 Nantes Cedex 3, France
Email:
Luc.Hillairet@math.univ-nantes.fr
Chris
Judge
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47401
Email:
cjudge@indiana.edu
DOI:
10.1090/S0002-9947-2010-04943-8
PII:
S 0002-9947(2010)04943-8
Received by editor(s):
March 3, 2008
Posted:
August 3, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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