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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
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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.