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.
Felli, V., Ognibene, R. (2020). Sharp convergence rate of eigenvalues in a domain with a shrinking tube. JOURNAL OF DIFFERENTIAL EQUATIONS, 269(1), 713-763 [10.1016/j.jde.2019.12.022].
Sharp convergence rate of eigenvalues in a domain with a shrinking tube
Felli V.
;Ognibene R.
2020
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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