On the principal eigenvalue of a Robin problem with a large parameter. (English) Zbl 1136.35060

Summary: 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.


35P15 Estimates of eigenvalues in context of PDEs
35P05 General topics in linear spectral theory for PDEs
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