An optimization problem for the first eigenvalue of the $p-$fractional laplacian
Analysis of PDEs
2017-03-31 v2
Abstract
In this paper we analyze an eigenvalue problem related to the nonlocal laplace operator plus a potential. After reviewing some elementary properties of the first eigenvalue of these operators (existence, positivity of associated eigenfunctions, simplicity and isolation) we investigate the dependance of the first eigenvalue on the potential function and establish the existence of some {\em optimal} potentials in some admissible classes.
Cite
@article{arxiv.1601.03019,
title = {An optimization problem for the first eigenvalue of the $p-$fractional laplacian},
author = {L. Del Pezzo and J. Fernandez Bonder and L. Lopez-Rios},
journal= {arXiv preprint arXiv:1601.03019},
year = {2017}
}
Comments
22 pages. Submitted