Asymptotic issue for fractional laplacian on long cylinders

2025/10/23 by Tahir Boudjeriou, Boudjeriou, Tahir, Prosenjit Roy +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2510.20263

openalex publication_date 2025/10/23 · openalex created_date 2025/10/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional p-Laplacian in cylindrical domains that become unbounded in one direction. The nonlocal nature of the operator describing the equations creates several technical difficulties in treating problems of this type. The main results, obtained within a nonlocal abstract framework, extend and complement related properties established in the local setting.

Citations

• Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction
• Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded
• Multiplicity results for the fractional laplacian in expanded domains

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• Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded
• Asymptotic behavior of solutions for nonlinear elliptic problems with\n the fractional Laplacian
• On nonlocal nonlinear elliptic problem with the fractional Laplacian
• Large solutions for fractional Laplacian operators