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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.

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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