English

Singularities of solutions of nonlocal nonlinear equations

Analysis of PDEs 2025-07-09 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2410.13292,
  title  = {Singularities of solutions of nonlocal nonlinear equations},
  author = {Minhyun Kim and Se-Chan Lee},
  journal= {arXiv preprint arXiv:2410.13292},
  year   = {2025}
}

Comments

Proof of 1-dimemsional case has been fixed. 39 pages