On the principal eigenvalue of a Robin problem with a large parameter
Levitin, M. and Parnovski, L. (2008) On the principal eigenvalue of a Robin problem with a large parameter. Mathematische Nachrichten, 281 (2). pp. 272-281. ISSN 0025-584X
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To link to this article DOI: 10.1002/mana.200510600
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.