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<p>In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional <i>p</i>-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.</p>

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Asymptotic Issues for Fractional Laplacian on Long Cylinders

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Tahir Boudjeriou,
  • Prosenjit Roy

摘要

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.