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

2004/03/10 by Michael Levitin, Levitin, Michael, Leonid Parnovski +1
Mathematics · #35P05 #35P15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P05 #msc:35P15

paper · pdf · doi:10.48550/arxiv.math/0403179

16 pages; no figures; replaces math.SP/0403179; completely re-written

arxiv created 2005/01/17 · arxiv updated 2009/12/01

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.

Related

• Laplacian eigenvalues with a large negative Robin parameter on a part of the boundary
• Principal eigenvalues and asymptotic behavior for the weighted p-Laplacian with Robin boundary conditions on exterior domains
• Optimizing the ground of a Robin Laplacian: asymptotic behavior
• Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters
• Laplacian eigenvalues for large negative Robin parameters on domains with outward peaks