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

Frank, Rupert L.; Larson, Simon (2020): On the error in the two-term Weyl formula for the Dirichlet Laplacian. In: Journal of Mathematical Physics, Vol. 61, No. 4

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 Rd. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-2488
• Language: English