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Type: yago:WikicatPartialDifferentialEquationsyago:Abstraction100002137yago:Communication100033020yago:DifferentialEquation106670521yago:Equation106669864yago:MathematicalStatement106732169yago:Message106598915yago:PartialDifferentialEquation106670866yago:Statement106722453 New Facet based on Instances of this Class

In mathematics, especially spectral theory, Weyl's law describes the asymptotic behavior of eigenvalues of the Laplace–Beltrami operator. This description was discovered in 1911 (in the case) by Hermann Weyl for eigenvalues for the Laplace–Beltrami operator acting on functions that vanish at the boundary of a bounded domain . In particular, he proved that the number, , of Dirichlet eigenvalues (counting their multiplicities) less than or equal to satisfies where is a volume of the unit ball in . In 1912 he provided a new proof based on variational methods.