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December 2005 Eigenvalue Problems on Domains with Cracks I
Kazushi YOSHITOMI
Tokyo J. Math. 28(2): 341-380 (December 2005). DOI: 10.3836/tjm/1244208195

Abstract

We study an eigenvalue problem for the Laplace operator on a planar region with a growing crack. We impose the Neumann boundary condition on the crack and the Dirichlet boundary condition elsewhere. One tip of the crack is fixed at the boundary. We obtain the full asymptotic expansions of the first two eigenvalues of that operator as the other tip of the crack reaches the boundary.

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Kazushi YOSHITOMI. "Eigenvalue Problems on Domains with Cracks I." Tokyo J. Math. 28 (2) 341 - 380, December 2005. https://doi.org/10.3836/tjm/1244208195

Information

Published: December 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1134.35319
MathSciNet: MR2191054
Digital Object Identifier: 10.3836/tjm/1244208195

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics

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Vol.28 • No. 2 • December 2005
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