Stability of variational eigenvalues for the fractional $p-$Laplacian
Copyright policy )Stability of variational eigenvalues for the fractional $p-$Laplacian
By virtue of $��-$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
- University of Ferrara Italy
- Aix-Marseille University France
- Catholic University of the Sacred Heart Italy
- University of Verona Italy
nonlocal eigenvalue problems, Methods involving semicontinuity and convergence; relaxation, critical points, Variational eigenvalues, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, eigenvalues; fractional p-Laplacian gamma-convergence, 35P30, 49J35, 49J45, Critical points; Fractional p-Laplacian; Nonlocal eigenvalue problems; Γ-convergence;, Mathematics - Analysis of PDEs, fractional \(p\)-Laplacian, FOS: Mathematics, Existence of solutions for minimax problems, fractional problems, \(\Gamma\)-convergence, Analysis of PDEs (math.AP)
nonlocal eigenvalue problems, Methods involving semicontinuity and convergence; relaxation, critical points, Variational eigenvalues, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, eigenvalues; fractional p-Laplacian gamma-convergence, 35P30, 49J35, 49J45, Critical points; Fractional p-Laplacian; Nonlocal eigenvalue problems; Γ-convergence;, Mathematics - Analysis of PDEs, fractional \(p\)-Laplacian, FOS: Mathematics, Existence of solutions for minimax problems, fractional problems, \(\Gamma\)-convergence, Analysis of PDEs (math.AP)
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