## 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

### Keywords:

Robin problem; Laplacian; asymptotic eigenvalue estimates
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### References:

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