@Article{ATA-36-243,
author = {Chen , Hua and Li , Jinning},
title = {Estimates of Dirichlet Eigenvalues for One-Dimensional Fractal Drums},
journal = {Analysis in Theory and Applications},
year = {2020},
volume = {36},
number = {3},
pages = {243--261},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-SU7},
url = {http://global-sci.org/intro/article_detail/ata/18285.html}
}