Year: 2020
Author: Hua Chen, Jinning Li
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 3 : pp. 243–261
Abstract
Let $\Omega$, with finite Lebesgue measure $|\Omega|$, be a non-empty open subset of $\mathbb{R}$, and $\Omega=\bigcup_{j=1}^\infty\Omega_j$, where the open sets $\Omega_j$ are pairwise disjoint and the boundary $\Gamma=\partial\Omega$ has Minkowski dimension $D\in (0,1)$. In this paper we study the Dirichlet eigenvalues problem on the domain $\Omega$ 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
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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]