Stability of variational eigenvalues for the fractional p-Laplacian

2015/03/13 by Lorenzo Brasco, Brasco, Lorenzo, Enea Parini +3 · 3 citations
Computer Science · Mathematics · #35P30 #49J35 #49J45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35P30 #msc:49J35 #msc:49J45

paper · pdf · doi:10.48550/arxiv.1503.04182

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

openalex publication_date 2015/03/13 · arxiv created 2022/02/23 · arxiv updated 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Fractional p-eigenvalues
• Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates

Cited by

• Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
• A note on the eigenvalues of fractional Hardy-Sobolev operator with indefinite weight
• The Brezis-Nirenberg problem for the fractional p-Laplacian

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