Asymptotic eigenvalue estimates for a Robin problem with a large parameter

Abstract

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.

This is an extended version of arXiv: 1312.7293~[math-ph], with more coauthors and the upper bound substantially improved; to appear in Portugalia Math

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