On the principal eigenvalue of a Robin problem with a large parameter |
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| Authors: | Michael Levitin Leonid Parnovski |
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| Affiliation: | 1. Department of Mathematics, Heriot‐Watt University, Riccarton, Edinburgh EH14 4AS, UK;2. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK;3. Phone: +44 207 679 2847, Fax: +44 207 383 55 19 |
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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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Robin problem generalised Neumann problem asymptotic analysis principal eigenvalue cones |
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