Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain
Rupert L. Frank, Simon Larson · Journal für die reine und angewandte Mathematik (Crelles Journal) · 2019
Abstract 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.