S. Larson

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math.SP2020

Semiclassical asymptotics for a class of singular Schrödinger operators

Rupert L. Frank, Simon Larson

Let $Ω \subset R^{d}$ be bounded with $C^{1}$ boundary. In this paper we consider Schrödinger operators $- Δ + W$ on $Ω$ with $W (x) \approx dist (x, \partial Ω)^{- 2}$ as $\m…

math.SP2020

On the error in the two-term Weyl formula for the Dirichlet Laplacian

Rupert L. Frank, Simon Larson

We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of $R^{d}$ . In particular, f…

math.SP2019

Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain

Rupert L. Frank, Simon Larson

We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex…