Can one see the fundamental frequency of a drum?
Maz'ya, Vladimir ; Shubin, Mikhail
arXiv, 0506181 / Harvested from arXiv
Text on arXiv
We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of G which is defined as the maximal possible radius of a ball B which has a negligible intersection with the complement of G. Here negligibility of a subset F in B means that the Wiener capacity of F does not exceed gamma times the capacity of B, where gamma is an arbitrarily fixed constant between 0 and 1. We provide explicit values of constants in the two-sided estimates.
Publié le : 2005-06-09
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  35P15 
@article{0506181,
     author = {Maz'ya, Vladimir and Shubin, Mikhail},
     title = {Can one see the fundamental frequency of a drum?},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506181}
}

Maz'ya, Vladimir; Shubin, Mikhail. Can one see the fundamental frequency of a drum?. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506181/