The Krein-von Neumann Realization of Perturbed Laplacians on Bounded Lipschitz Domains

TL;DR

This paper characterizes the Krein-von Neumann realization of perturbed Laplacians on Lipschitz domains, providing explicit boundary domain descriptions and establishing eigenvalue asymptotics.

Contribution

It offers a detailed boundary domain description and Weyl asymptotics for the Krein-von Neumann realization of perturbed Laplacians on Lipschitz domains.

Findings

Explicit boundary domain description in terms of boundary traces

Weyl asymptotic formula for eigenvalues

Self-contained analysis of the Krein-von Neumann realization

Abstract

In this paper we study the self-adjoint Krein-von Neumann realization $A_K$ of the perturbed Laplacian $-\Delta+V$ in a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$. We provide an explicit and self-contained description of the domain of $A_K$ in terms of Dirichlet and Neumann boundary traces, and we establish a Weyl asymptotic formula for the eigenvalues of $A_K$.