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

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

2004-03-10

arxiv.org/abs/math/0403179v2

Mathematics

Spectral Theory

16 pages; no figures; replaces math.SP/0403179; completely re-written

Scientific paper

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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