Neumann to Steklov eigenvalues: asymptotic and monotonicity results
Abstract
We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behavior of the Neumann eigenvalues and find explicit formulas for their derivatives at the limiting problem. We deduce that the Neumann eigenvalues have a monotone behavior in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.
Keywords
Cite
@article{arxiv.1602.06078,
title = {Neumann to Steklov eigenvalues: asymptotic and monotonicity results},
author = {Pier Domenico Lamberti and Luigi Provenzano},
journal= {arXiv preprint arXiv:1602.06078},
year = {2016}
}
Comments
This paper has been accepted for publication in Proceedings of the Royal Society of Edinburgh Section A Mathematics and will appear in a revised form subsequent to editorial input by the ICMS/Royal Soc. of Edinburgh. Material on these pages is copyright Cambridge University Press. http://www.rsescotlandfoundation.org.uk/proceedings-a-mathematics.html journals.cambridge.org/action/displayJournal?jid=PRM