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Estimates of Dirichlet Eigenvalues for One-Dimensional Fractal Drums

Year:    2020

Author:    Hua Chen, Jinning Li

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 3 : pp. 243–261

Abstract

Let Ω, with finite Lebesgue measure |Ω|, be a non-empty open subset of R, and Ω=j=1Ωj, where the open sets Ωj are pairwise disjoint and the boundary Γ=Ω has Minkowski dimension D(0,1). In this paper we study the Dirichlet eigenvalues problem on the domain Ω and give the exact second asymptotic term for the eigenvalues, which is related to the Minkowski dimension D. Meanwhile, we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-SU7

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 3 : pp. 243–261

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    One-dimensional fractal drum Dirichlet eigenvalues Pόlya conjecture Minkowski dimension.

Author Details

Hua Chen Email

Jinning Li Email

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    https://doi.org/10.1016/j.jde.2022.09.021 [Citations: 4]