{
  "id": "2401.02186",
  "version": "v1",
  "published": "2024-01-04T10:37:09.000Z",
  "updated": "2024-01-04T10:37:09.000Z",
  "title": "Regularity for multi-phase problems at nearly linear growth",
  "authors": [
    "Filomena De Filippis",
    "Mirco Piccinini"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "Minima of the log-multiphase variational integral $$ w \\mapsto \\int_{\\Omega} \\left[|Dw|\\log(1+|Dw|) + a(x)|Dw|^q + b(x)|Dw|^s\\right] \\, {\\rm d}x\\,, $$ have locally H\\\"older continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the H\\\"older exponents of the modulating coefficients $a(\\cdot)$ and $b(\\cdot)$ respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-04T10:37:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N60",
      "35J60"
    ],
    "keywords": [
      "linear growth",
      "multi-phase problems",
      "regularity",
      "log-multiphase variational integral",
      "growth powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}