The Robin Laplacian in the large coupling limit: Convergence and spectral asymptotic

TL;DR

This paper investigates the behavior of Robin Laplacians as the coupling parameter becomes large, providing convergence rates, asymptotic expansions, and applications to the unit disc.

Contribution

It offers new asymptotic expansions and convergence analysis for Robin Laplacians in the large coupling limit, including explicit results for the unit disc.

Findings

Convergence of resolvent differences with explicit rates

Asymptotic expansions for eigenvalues and eigenprojections

Application to the spectral analysis of the unit disc

Abstract

We study convergence modes as well as their respective rates for the resolvent difference of Robin and Dirichlet Laplacian on bounded smooth domains in the large coupling limit. Asymptotic expansions for the resolvent, the eigenprojections and the eigenvalues of the Robin Laplacian are performed. Finally we apply our results to the case of the unit disc.