Asymptotic issue for fractional laplacian on long cylinders

TL;DR

This paper studies the asymptotic behavior of solutions to fractional p-Laplacian problems in long cylindrical domains, addressing nonlocal challenges and extending local results to a nonlocal framework.

Contribution

It introduces a nonlocal abstract framework to analyze asymptotics of fractional p-Laplacian problems in unbounded cylinders, expanding understanding beyond local cases.

Findings

Extended asymptotic properties for fractional p-Laplacian in cylinders

Developed nonlocal analytical framework for unbounded domains

Addressed technical challenges of nonlocal operators in elongated domains

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.