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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Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation
Chen, Hua
Chen, Hong-Ge
Yuan, Xin-Rui
Journal of Differential Equations, Vol. 341 (2022), Iss. P.504
https://doi.org/10.1016/j.jde.2022.09.021 [Citations: 4]