# 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} }

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…

## 27 Citations

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