JournalspmVol. 71, No. 2pp. 141–156

Asymptotic eigenvalue estimates for a Robin problem with a large parameter

  • Pavel Exner

    Doppler Institute for Mathematical Physics and Applied Mathematics, Prague, Czech Republic

  • Alexander Minakov

    Mathematical Physics and Applied Mathematics, Prague, Czech Republic

  • Leonid Parnovski

    University College London, UK
Asymptotic eigenvalue estimates for a Robin problem with a large parameter cover
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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.

Cite this article

Pavel Exner, Alexander Minakov, Leonid Parnovski, Asymptotic eigenvalue estimates for a Robin problem with a large parameter. Port. Math. 71 (2014), no. 2, pp. 141–156

DOI 10.4171/PM/1945