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

Rupert L. Frank; Simon Larson

doi:10.1063/1.5145003

paper

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

arXiv:2001.01876 · doi:10.1063/1.5145003

Abstract

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, for the short-time asymptotics of the trace of the heat kernel we prove that the error term cannot be made quantitatively better than little- $o$ of the second term.

19 pages