Can one see the fundamental frequency of a drum?
2005 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, Vol. 74, no 2, 135-151 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:liu:diva-35982DOI: 10.1007/s11005-005-0010-1Local ID: 29255OAI: oai:DiVA.org:liu-35982DiVA: diva2:256830