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

Creators: Frank, Rupert L.; Larson, Simon

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.

Additional Information

© 2020 Published under license by AIP Publishing. Submitted: 13 January 2020; Accepted: 24 March 2020; Published Online: 20 April 2020. We would like to dedicate this paper to the memory of Jean Bourgain. The U.S. National Science Foundation (Grant No. DMS-1363432) (R.L.F.) and Knut and Alice Wallenberg Foundation (Grant No. KAW 2018.0281) (S.L.) are acknowledged. The authors also wish to thank Institut Mittag-Leffler, where part of this work was carried out. Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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