Can one see the fundamental frequency of a drum?

• We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set Ω⊂ℝn 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 ⊂ B means that cap(F)≤γ cap (B), where cap a means the Wiener (harmonic) capacity and γ is arbitrarily fixed with the sole restriction 0 < γ < 1. We provide explicit values of constants in the two-sided estimates. © Springer 2005.

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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MATHEMATICS

MATEMATIK

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