{
  "id": "2410.19970",
  "version": "v1",
  "published": "2024-10-25T21:07:05.000Z",
  "updated": "2024-10-25T21:07:05.000Z",
  "title": "Improved regularity estimates for Hardy-Hénon-type equations driven by the $\\infty$-Laplacian",
  "authors": [
    "Elzon C. Bezerra Júnior",
    "João Vitor da Silva",
    "Thialita M. Nascimento",
    "Ginaldo S. Sá"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-H\\'{e}non-type equations with possibly singular weights and strong absorption governed by the $\\infty$-Laplacian $$ \\Delta_{\\infty} u(x) = |x|^{\\alpha}u_+^m(x) \\quad \\text{in} \\quad B_1, $$ under suitable assumptions on the data. In this setting, we derive an explicit regularity exponent that depends only on universal parameters. Additionally, we prove non-degeneracy properties, providing further geometric insights into the nature of these solutions. Our regularity estimates not only improve but also extend, to some extent, the previously obtained results for zero-obstacle and dead-core problems driven by the $\\infty$-Laplacian. As an application of our findings, we also address some Liouville-type results for this class of equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-25T21:07:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J60",
      "35J94"
    ],
    "keywords": [
      "regularity estimates",
      "hardy-hénon-type equations driven",
      "dead-core problems driven",
      "explicit regularity exponent",
      "viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}