Spectral stability of the \(\overline{\partial}\)-Neumann Laplacian: the Kohn-Nirenberg elliptic regularization (Q2024697)

The authors continue the first and third authors' work from 2019 [``Spectral stability of the \(\overline\partial\)-Neumann Laplacian: domain perturbations'', Preprint, \url{arXiv:1908.03256}]. Let \(\square_q\) be the \(\overline{\partial}\)-Neumann Laplacian on \((p,q)\)-forms on a bounded domain \(\Omega\), and let \(\square_q^t\) denote its Kohn-Nirenberg regularization. The authors study how the variational eigenvalues of these operators change when \(t\) changes or when \(\Omega\) changes. They present quantitative results on the eigenvalues in terms of the perturbations. It is a well-written paper that would be relevant to anyone interested in the spectral theory of \(\overline{\partial}\)-Neumann Laplacian and overall subelliptic differential operators.