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On the remainder in the Weyl formula for the Euclidean disk. (English) Zbl 1379.35207
Actes de Séminaire de Théorie Spectrale et Géométrie. Année 2010–2011. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Séminaire de Théorie Spectrale et Géométrie 29, 1-13 (2011).
Summary: We prove a 2-terms Weyl formula for the counting function \(N(\mu)\) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimates \(O(\mu^{2/3})\).
For the entire collection see [Zbl 1356.35008].

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
11P21 Lattice points in specified regions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
58J05 Elliptic equations on manifolds, general theory
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