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

Frank, Rupert L. and 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

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0075-4102
• Language: English