Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems

Abstract

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.