Abstract
Virtually all results on eigenvalue asymptotics for differential operators have their roots in Weyl’s celebrated law for the distribution of the eigenvalues
of the Dirichlet Laplacian -△ on an open, bounded domain Ω ⊂ Rm: If N(λ) denotes the number of eigenvalues E k < λ, then
under mild regularity assumptions on the boundary δΩ here c m is a universal constant which depends only on the dimension m.
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Hempel, R. (1997). On the Asymptotic Distribution of Eigenvalues in Gaps. In: Rauch, J., Simon, B. (eds) Quasiclassical Methods. The IMA Volumes in Mathematics and its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1940-8_5
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