Stability of variational eigenvalues for the fractional p-Laplacian

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.

35 pages. Theorem 2.10 has been expanded, Appendix B has been added

References in corpus (1)

• Gamma-convergence of nonlocal perimeter functionals

Cited by in corpus (2)

• The Brezis-Nirenberg problem for the fractional $p$-Laplacian
• A note on the eigenvalues of fractional Hardy-Sobolev operator with indefinite weight