Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues
Spectral Theory
2014-10-03 v1
Abstract
We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the dependence of the eigenvalues of the Steklov problem upon perturbation of the mass density and show that the Steklov eigenvalues violates a maximum principle in spectral optimization problems.
Keywords
Cite
@article{arxiv.1410.0517,
title = {Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues},
author = {Pier Domenico Lamberti and Luigi Provenzano},
journal= {arXiv preprint arXiv:1410.0517},
year = {2014}
}
Comments
This is a preprint version of a paper that will appear in the Proceedings of the 9th ISAAC Congress, Krak\'ow 2013