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

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 $A_K$.