{
  "id": "2410.15782",
  "version": "v1",
  "published": "2024-10-21T08:47:57.000Z",
  "updated": "2024-10-21T08:47:57.000Z",
  "title": "Boundary estimates for harmonic functions in $C^1$ domains",
  "authors": [
    "Clara Torres-Latorre"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain boundary nondegeneracy and regularity estimates for harmonic functions in $C^1$ domains, providing an explicit modulus of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with $C^{1,\\mathrm{Dini}}$ boundaries, while also recovering the known $C^{1-\\varepsilon}$ regularity for flat Lipschitz domains, unifying both theories with a single proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-21T08:47:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B25",
      "35B65",
      "35J25"
    ],
    "keywords": [
      "harmonic functions",
      "boundary estimates",
      "boundary lipschitz regularity",
      "flat lipschitz domains",
      "results extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}