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

## TL;DR

This paper investigates how the spectrum of the $ar ext{ extdollar} ext{ extdollar}$-Neumann Laplacian remains stable under perturbations of the domain or the operator, using Kohn-Nirenberg elliptic regularization to provide quantitative estimates.

## Contribution

It introduces a new approach to quantify spectral stability of the $ar ext{ extdollar} ext{ extdollar}$-Neumann Laplacian under perturbations via Kohn-Nirenberg regularization.

## Key findings

- Quantitative estimates for spectral stability under domain perturbations
- Quantitative estimates for spectral stability under operator perturbations
- Enhanced understanding of the spectral behavior of the $ar ext{ extdollar} ext{ extdollar}$-Neumann Laplacian

## 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.