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<p>This paper investigates a gradient-degenerate, nonlocal version of the generalized <i>p</i>-Laplacian introduced by Baravdish, Cheng, Svensson, and Åström <CitationRef CitationID="CR7">2020</CitationRef>. A key feature of this operator is its degeneracy along the set of critical points, which prevents the application of standard comparison principles. We establish the existence and interior Lipschitz regularity of viscosity solutions by employing an adapted Ishii-Lions “doubling variables” technique. We also identify a setting in which uniqueness of solutions is proved.</p>

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Viscosity solutions to nonlocal generalized p-Laplacian: existence, uniqueness, and regularity

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Priyank Oza,
  • Durvudkhan Suragan

摘要

This paper investigates a gradient-degenerate, nonlocal version of the generalized p-Laplacian introduced by Baravdish, Cheng, Svensson, and Åström 2020. A key feature of this operator is its degeneracy along the set of critical points, which prevents the application of standard comparison principles. We establish the existence and interior Lipschitz regularity of viscosity solutions by employing an adapted Ishii-Lions “doubling variables” technique. We also identify a setting in which uniqueness of solutions is proved.