{
  "id": "2403.02964",
  "version": "v2",
  "published": "2024-03-05T13:40:55.000Z",
  "updated": "2024-07-11T10:45:35.000Z",
  "title": "Balayage of measures: behavior near a corner",
  "authors": [
    "Christophe Charlier",
    "Jonatan Lenells"
  ],
  "comment": "Results are improved; 19 pages, 6 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the balayage of a measure $\\mu$ defined on a domain $\\Omega$ onto its boundary $\\partial \\Omega$. Assuming that $\\Omega$ has a corner of opening $\\pi \\alpha$ at a point $z_0 \\in \\partial \\Omega$ for some $0 < \\alpha \\leq 2$ and that $d\\mu(z) \\asymp |z-z_{0}|^{2b-2}d^{2}z$ as $z\\to z_0$ for some $b > 0$, we obtain the precise rate of vanishing of the balayage of $\\mu$ near $z_{0}$. The rate of vanishing is universal in the sense that it only depends on $\\alpha$ and $b$. We also treat the case when the domain has multiple corners at the same point. Moreover, when $2b\\leq \\frac{1}{\\alpha}$, we provide explicit constants for the upper and lower bounds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-11T10:45:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bounds",
      "multiple corners",
      "explicit constants",
      "precise rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}