L. Del Pezzo, J. Fernandez Bonder, L. Lopez-Rios
Published 2016-01-12Version 1
In this paper we analyze an eigenvalue problem related to the nonlocal $p-$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.
Comments: 22 pages. Submitted
On the strict monotonicity of the first eigenvalue of the $p$-Laplacian on annuli
Eigenvalue Problems in $\mathrm{L}^\infty$: Optimality Conditions, Duality, and Relations with Optimal Transport
The $\infty$-eigenvalue problem with a sign-changing weight
![QR code for arXiv:1601.03019 [math.AP]](http://oss.arxitics.com/images/favicon.svg)