Calculus of Variations and Geometric Measure Theory

L. Brasco - E. Parini - M. Squassina

Stability of variational eigenvalues for the fractional $p-$Laplacian

created by brasco on 13 Mar 2015
modified on 24 Aug 2015


Accepted Paper

Inserted: 13 mar 2015
Last Updated: 24 aug 2015

Journal: Discrete Contin. Dyn. Syst.
Pages: 35
Year: 2015


By virtue of $\Gamma-$convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional $p-$Laplacian operator, in the singular limit as the nonlocal operator converges to the $p-$Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.

Keywords: Gamma-convergence, critical points, nonlocal eigenvalue problems, Fractional p-Laplacian