Asymptotic eigenvalue estimates for a Robin problem with a large parameter
Pavel Exner, Alexander Minakov, Leonid Parnovski · Portugaliae Mathematica · 2014
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.