Work

Convergence rates of eigenvalue problems in perforated domains: the case of small volume

Year: 2025

Type: article

Abstract: This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral gaps for an asymptotic expansion, with two leading terms, of Dirichlet eigenvalues. We also establish the convergence rates for the corresponding eigenfunctions. Our approach uses a known reduction to a degenerate elliptic eigenvalue problem for which a quantitative analysis is carried out.

Source: Advanced Nonlinear Studies

DOI: 10.1515/ans-2023-0166

Authors: Zhongwei Shen, Jinping Zhuge

Institutions: University of Kentucky, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,469

OpenAlex ID: W4407498564

FWCI:

Cites: 11

Cited by:

Related to: 10