The Neumann eigenvalue problem for the $\infty$-Laplacian
Analysis of PDEs
2014-09-23 v2
Abstract
The first nontrivial eigenfunction of the Neumann eigenvalue problem for the -Laplacian, suitable normalized, converges as goes to to a viscosity solution of an eigenvalue problem for the -Laplacian. We show among other things that the limit of the eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.
Cite
@article{arxiv.1405.3535,
title = {The Neumann eigenvalue problem for the $\infty$-Laplacian},
author = {L. Esposito and B. Kawohl and C. Nitsch and C. Trombetti},
journal= {arXiv preprint arXiv:1405.3535},
year = {2014}
}
Comments
Corrected few typos. Corollary 5 added