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 a two term asymptotics in terms of the coupling constant and the maximum of the boundary curvature.
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Pavel Exner, Alexander Minakov, Leonid Parnovski, Asymptotic eigenvalue estimates for a Robin problem with a large parameter. Port. Math. 71 (2014), no. 2, pp. 141–156DOI 10.4171/PM/1945