{
  "id": "2405.11747",
  "version": "v1",
  "published": "2024-05-20T03:13:00.000Z",
  "updated": "2024-05-20T03:13:00.000Z",
  "title": "Wolff potentials and nonlocal equations of Lane-Emden type",
  "authors": [
    "Quoc-Hung Nguyen",
    "Jihoon Ok",
    "Kyeong Song"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider nonlocal equations of the type \\[ (-\\Delta_{p})^{s}u = \\mu \\quad \\text{in }\\Omega, \\] where $\\Omega \\subset \\mathbb{R}^{n}$ is either a bounded domain or the whole $\\mathbb{R}^{n}$, $\\mu$ is a Radon measure on $\\Omega$, $0<s<1$ and $1<p<n/s$. Especially, we extend the existence, regularity and Wolff potential estimates for SOLA (Solutions Obtained as Limits of Approximations), established by Kuusi, Mingione, and Sire (Comm. Math. Phys. 337:1317--1368, 2015), to the strongly singular case $1<p\\le2-s/n$. Moreover, using Wolff potentials and Orlicz capacities, we present both a sufficient and a necessary conditions for the existence of SOLA to nonlocal equations of the type \\[ (-\\Delta_{p})^{s}u = P(u) + \\mu \\quad \\text{in }\\Omega, \\] where $P(\\cdot)$ is either a power function or an exponential function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-20T03:13:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlocal equations",
      "lane-emden type",
      "wolff potential estimates",
      "radon measure",
      "orlicz capacities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}