Stability of variational eigenvalues for the fractional p−Laplacian

Lorenzo Brasco (1) , Enea Parini (1) , Marco Squassina (2)

1 I2M - Institut de Mathématiques de Marseille
2 UNIVR | DI - Department of Computer Science [Verona]

By virtue of Γ−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.

Mots clés: Fractional p-Laplacian; critical points; nonlocal eigenvalue problems; Gamma-convergence

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Enea Parini, Marco Squassina. Stability of variational eigenvalues for the fractional p−Laplacian. Discrete and Continuous Dynamical Systems - Series A, 2016, 36, pp.1813-1845. ⟨10.3934/dcds.2016.36.1813⟩. ⟨hal-01131731⟩