Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimization problem for the first eigenvalue of the $p-$fractional
  laplacian   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.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an