{
  "id": "2408.11555",
  "version": "v1",
  "published": "2024-08-21T12:06:52.000Z",
  "updated": "2024-08-21T12:06:52.000Z",
  "title": "Improved moduli of continuity for degenerate phase transitions",
  "authors": [
    "Ugo Gianazza",
    "Naian Liao",
    "José Miguel Urbano"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N$-dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\\geq 3$, we sharpen it to $$ \\boldsymbol{\\omega}(r) \\approx \\exp (-c| \\ln r|^{\\frac1N}); $$ for $p>\\max\\{2,N\\}$, we derive an unexpected H\\\"older modulus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-21T12:06:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "35K92",
      "35B65",
      "76S05",
      "80A22"
    ],
    "keywords": [
      "degenerate phase transitions",
      "continuity",
      "current state-of-the-art modulus",
      "weak solutions",
      "degenerate diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}