Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains

• 成果类型: Article
• 署名作者: Frank, Rupert L.; Larson, Simon
• 署名单位: University of Munich; California Institute of Technology; Chalmers University of Technology; University of Gothenburg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01352-x
• 发表日期: 2025
• 页码: 999-1079
• 关键词: sharp spectral asymptotics; irregular coefficients; eigenvalues; Operators; BOUNDARY; formulas; BEHAVIOR; equation; kernel; shape

摘要

We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems.