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Can one see the fundamental frequency of a drum?

Maz´ya, Vladimir G., 1937- (author)
Linköpings universitet,Tekniska högskolan,Tillämpad matematik
Shubin, Mikhail (author)
 (creator_code:org_t)
2005-11-15
2005
English.
In: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 74:2, s. 135-151
  • Journal article (peer-reviewed)
Abstract Subject headings
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  • 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)
NATURAL SCIENCES  -- Mathematics (hsv//eng)

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MATHEMATICS
MATEMATIK

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ref (subject category)
art (subject category)

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