Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems

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

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES

Lugar: springfield; Año: 2021 vol. 41 p. 2125 - 2140

1078-0947

In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of the eigenvalues of the p−fractional laplacian when the fractional parameter s goes to 1, and to extend some known results for the behavior of the same eigenvalue problem when p goes to ∞. Finally we analyze other eigenvalue problems not previously covered in the literature