# Can One See the Fundamental Frequency of a Drum?

@article{Mazya2005CanOS,
title={Can One See the Fundamental Frequency of a Drum?},
author={Vladimir Maz'ya and Mikhail A. Shubin},
journal={Letters in Mathematical Physics},
year={2005},
volume={74},
pages={135-151}
}
• Published 9 June 2005
• Mathematics, Physics
• Letters in Mathematical Physics
AbstractWe establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set $$\Omega \subset \mathbb{R}^n$$ with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of Ω which is defined as the maximal possible radius of a ball B with a negligible intersection with the complement of Ω. Here negligibility of $$F\subset B$$ means that cap(F)≤ γ cap (B), where cap a means the Wiener (harmonic) capacity and…
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