Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems

FERNÁNDEZ BONDER, JULIÁN; SILVA, ANALÍA; F. SPEDALETTI, JUAN

Discrete & Continuous Dynamical Systems - A

American Institute of Mathematics

Año: 2020 vol. 0 p. 1 - 16

1553-5231

In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. Thismethod allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of theeigenvalues of the p−fractional laplacian when the fractional parameter s goesto 1, and to extend some known results for the behavior of the same eigenvalueproblem when p goes to ∞. Finally we analyze other eigenvalue problems notpreviously covered in the literature.