Can One See the Fundamental Frequency of a Drum?

  title={Can One See the Fundamental Frequency of a Drum?},
  author={Vladimir Maz'ya and Mikhail A. Shubin},
  journal={Letters in Mathematical Physics},
  • V. Maz'ya, M. Shubin
  • 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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