Stability of complement value problems for p-Lévy operators

2023/03/07 by Guy Foghem, Foghem, Guy · 2 citations
Computer Science · Mathematics · #35B35 #35D30 #35J60 #35J66 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2303.03776

openalex publication_date 2023/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear integrodifferential p-Lévy operators. A prototypical example of integrodifferential p-Lévy operators is the well-known fractional p-Laplace operator. Our main focus is on nonlinear IDEs in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional p-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge a gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with p-Laplacian are strong limits of the nonlocal ones.

Cited by

• Nonlocal Dirichlet problems involving the Logarithmic p-Laplacian
• Sharp embeddings and existence results for Logarithmic p-Laplacian equations with critical growth

Related

• Remarks on the nonlocal Dirichlet problem
• Regularity results of nonlinear perturbed stable-like operators
• Nonlocal operators of order near zero
• Non-symmetric stable operators: regularity theory and integration by parts
• Global Hölder regularity for the fractional p-Laplacian