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Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth

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arxiv 2311.01246 v1 pith:NS55CM74 submitted 2023-11-02 math.AP

Minhyun Kim , Se-Chan Lee This is my paper · ORCID
classification math.AP
keywords nonlocalfunctionssuperharmonicsupersolutionsgrowthoperatorsorliczproblems
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We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal nonlinear potential theory. We provide several fine properties of supersolutions and superharmonic functions, and reveal the relation between them. Along the way we prove some results for nonlocal obstacle problems such as the well-posedness and (both interior and boundary) regularity estimates, which are of independent interest.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Capacitary estimates for solutions to nonlocal Dirichlet problems

    math.AP 2026-08 conditional novelty 7.0 of 10

    For nonlocal p-Laplace type equations with measurable coefficients, boundary Hölder regularity holds exactly when the exterior capacity density condition holds, with a quantitative modulus estimate.

  2. Liouville theorem for singular solutions to nonlocal equations

    math.AP 2025-07 conditional novelty 7.0 of 10

    Every singular solution to a nonlocal linear equation with measurable kernel that is one-sided bounded near zero and infinity must equal a multiple of the fundamental solution plus a constant.

  3. Semiregular and strongly irregular boundary points for nonlocal Dirichlet problems

    math.AP 2025-06 accept novelty 7.0 of 10

    Every irregular boundary point for fractional (s,p)-Laplace Dirichlet problems is either semiregular or strongly irregular, never both or neither.

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