{
  "id": "2302.05649",
  "version": "v1",
  "published": "2023-02-11T10:42:21.000Z",
  "updated": "2023-02-11T10:42:21.000Z",
  "title": "Regularity theory for parabolic systems with Uhlenbeck structure",
  "authors": [
    "Jihoon Ok",
    "Giovanni Scilla",
    "Bianca Stroffolini"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish local regularity theory for parabolic systems of Uhlenbeck type with $\\varphi$-growth. In particular, we prove local boundedness of weak solutions and their gradient, and then local H\\\"older continuity of the gradients, providing suitable assumptions on the growth function $\\varphi$. Our approach, being independent of the degeneracy of the system, allows for a unified treatment of both the degenerate and the singular case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-11T10:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K40",
      "46E35",
      "49N60"
    ],
    "keywords": [
      "parabolic systems",
      "uhlenbeck structure",
      "establish local regularity theory",
      "uhlenbeck type",
      "local boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}