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

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.

arXiv comment35 pages

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Cited by in corpus (7)

• On the error in the two-term Weyl formula for the Dirichlet Laplacian
• Semiclassical bounds for spectra of biharmonic operators
• Approximate normalizations for approximate density functionals
• On the spectral asymptotics for the buckling problem
• Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit
• Two consequences of Davies's Hardy inequality
• Weyl's law for Neumann Schrödinger operators on Hölder domains