An optimization problem for the first eigenvalue of the p-fractional Laplacian

FERNÁNDEZ BONDER, JULIÁN; LÓPEZ RÍOS, LUIS; DEL PEZZO, LEANDRO

MATHEMATISCHE NACHRICHTEN

WILEY-V C H VERLAG GMBH

Año: 2018 vol. 291 p. 632 - 651

0025-584X

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 dependence of the first eigenvalue on the potential function and establish the existence of some optimal potentials in some admissible classes.