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On the principal eigenvalue of a Robin problem with a large parameter
Author(s) -
Levitin Michael,
Parnovski Leonid
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510600
Subject(s) - mathematics , eigenvalues and eigenvectors , robin boundary condition , gravitational singularity , boundary (topology) , domain (mathematical analysis) , principal (computer security) , laplace operator , variety (cybernetics) , boundary value problem , neumann boundary condition , term (time) , piecewise , mathematical analysis , statistics , physics , quantum mechanics , computer science , operating system
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)