Calculus of Variations and Geometric Measure Theory

V. Felli - R. Ognibene

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

created by ognibene on 15 Oct 2021


Published Paper

Inserted: 15 oct 2021

Journal: Journal of Differential Equations
Year: 2020

ArXiv: 1809.02991 PDF


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.