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

Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265 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 doi: 10.1002/mana.200510600

Abstract/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.