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Frank, Rupert L.; Larson, Simon (2020): Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. In: Journal für die Reine und Angewandte Mathematik, Vol. 766: pp. 195-228
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We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.