Sharp Convergence Rate of Eigenvalues in a Domain with a Shrinking Tube
Analysis of PDEs
2018-09-11 v1
Abstract
In this paper we consider a class of singularly perturbed domains, obtained by attaching a cylindrical tube to a fixed bounded region and letting its section shrink to zero. We use an Almgren-type monotonicity formula to evaluate the sharp convergence rate of perturbed simple eigenvalues, via Courant-Fischer Min-Max characterization and blow-up analysis for scaled eigenfunctions.
Keywords
Cite
@article{arxiv.1809.02991,
title = {Sharp Convergence Rate of Eigenvalues in a Domain with a Shrinking Tube},
author = {Veronica Felli and Roberto Ognibene},
journal= {arXiv preprint arXiv:1809.02991},
year = {2018}
}
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36 pages