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On the principal eigenvalue of a Robin problem with a large parameter

Michael Levitin·Leonid Parnovski
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Abstract

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

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Michael Levitin, Leonid Parnovski. 2005-01-17. On the principal eigenvalue of a Robin problem with a large parameter. https://arxiv.org/abs/math/0403179

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