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Asymptotic eigenvalue estimates for a Robin problem with a large parameter. (English) Zbl 1295.35346

Summary: The Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a large parameter in the boundary condition is considered. We prove a two-sided three-term asymptotic estimate for the negative eigenvalues. Furthermore, improving the upper bound we get two term asymptotics in terms of the coupling constant and the maximum of the boundary curvature.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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