Calculus of Variations and Geometric Measure Theory
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V. Felli - R. Ognibene

Sharp convergence rate of eigenvalues in a domain with a shrinking tube

created by ognibene on 15 Oct 2021

[BibTeX]

Published Paper

Inserted: 15 oct 2021

Journal: Journal of Differential Equations
Year: 2020
Doi: https://doi.org/10.1016/j.jde.2019.12.022

ArXiv: 1809.02991 PDF

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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