Sharp Convergence Rate of Eigenvalues in a Domain with a Shrinking Tube

2018/09/09 by Felli, Veronica, Ognibene, Roberto
#35J25 #35P15 #35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.02991

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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