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Can one see the fundamental frequency of a drum?
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2005 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, Vol. 74, no 2, 135-151 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2005. Vol. 74, no 2, 135-151 p.
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URN: urn:nbn:se:liu:diva-35982DOI: 10.1007/s11005-005-0010-1Local ID: 29255OAI: diva2:256830
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-12

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Maz´ya, Vladimir G.
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The Institute of TechnologyApplied Mathematics
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