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Singularities of solutions of nonlocal nonlinear equations

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arxiv 2410.13292 v2 pith:RW4XXMXK submitted 2024-10-17 math.AP

Minhyun Kim , Se-Chan Lee This is my paper · ORCID
classification math.AP
keywords solutionsbehaviorequationsnonlinearnonlocalsingularitiesweakasymptotic
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We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution.

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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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