Stability of variational eigenvalues
for the fractional $p-$Laplacian
Lorenzo Brasco - Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frédéric Joliot Curie, 13453 Marseille, France (email)
Abstract: 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: Fractional $p-$Laplacian, nonlocal eigenvalue problems, critical points, $\Gamma-$convergence.
Received: March 2015; Revised: May 2015; Available Online: September 2015.
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