Spectral Stability of the $\bar\partial-$Neumann Laplacian: the Kohn-Nirenberg elliptic regularization

Abstract

In this paper we study spectral stability of the $\bar\partial$-Neumann Laplacian under the Kohn-Nirenberg elliptic regularization. We obtain quantitative estimates for stability of the spectrum of the $\bar\partial$-Neumann Laplacian when either the operator or the underlying domain is perturbed.