Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain

@article{Frank2019TwotermSA,
  title={Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain},
  author={Rupert L. Frank and Simon Larson},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year={2019},
  volume={2020},
  pages={195 - 228}
}
  • R. Frank, Simon Larson
  • Published 28 January 2019
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
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. 

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