Published Paper

Inserted: 15 oct 2021

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

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.