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

Rupert L. Frank; Simon Larson

doi:10.1063/1.5145003

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arXiv · 2001.01876

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

Rupert L. Frank·Simon Larson

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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 $\mathbb{R}^d$. 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.

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BibTeX RIS

Rupert L. Frank, Simon Larson. 2020-01-07. On the error in the two-term Weyl formula for the Dirichlet Laplacian. https://doi.org/10.1063/1.5145003

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