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

Michael Levitin; Leonid Parnovski

doi:10.1002/mana.200510600

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

Michael Levitin
, Leonid Parnovski

Research output: Contribution to journal › Article › peer-review

67 Citations (Scopus)

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.

Original language	English
Pages (from-to)	272-281
Number of pages	10
Journal	Mathematische Nachrichten
Volume	281
Issue number	2
DOIs	https://doi.org/10.1002/mana.200510600
Publication status	Published - Feb 2008

Keywords

Asymptotic analysis
Cones
Generalised Neumann problem
Principal eigenvalue
Robin problem

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10.1002/mana.200510600

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AB - 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.

KW - Asymptotic analysis

KW - Cones

KW - Generalised Neumann problem

KW - Principal eigenvalue

KW - Robin problem

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

Abstract

Keywords

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