{
  "id": "1401.2623",
  "version": "v1",
  "published": "2014-01-12T13:13:42.000Z",
  "updated": "2014-01-12T13:13:42.000Z",
  "title": "A quantitative modulus of continuity for the two-phase Stefan problem",
  "authors": [
    "Paolo Baroni",
    "Tuomo Kuusi",
    "José Miguel Urbano"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive the quantitative modulus of continuity $$ \\omega(r)=\\left[ p+\\ln \\left( \\frac{r_0}{r} \\right) \\right]^{-\\alpha (n,p)}, $$ which we conjecture to be optimal, for solutions of the $p$-degenerate two-phase Stefan problem. Even in the classical case $p=2$, this represents a twofold improvement with respect to the 1984 state-of-the-art result by DiBenedetto and Friedman [J. reine angew. Math., 1984], in the sense that we discard one logarithm iteration and obtain an explicit value for the exponent $\\alpha (n,p)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-12T13:13:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35K65",
      "80A22"
    ],
    "keywords": [
      "quantitative modulus",
      "continuity",
      "degenerate two-phase stefan problem",
      "reine angew",
      "state-of-the-art result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-014-0762-9",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2014,
      "month": "Nov",
      "volume": 214,
      "number": 2,
      "pages": 545
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014ArRMA.214..545B"
    }
  }
}