{
  "id": "2312.04220",
  "version": "v1",
  "published": "2023-12-07T11:10:56.000Z",
  "updated": "2023-12-07T11:10:56.000Z",
  "title": "Higher integrability for singular doubly nonlinear systems",
  "authors": [
    "Kristian Moring",
    "Leah Schätzler",
    "Christoph Scheven"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \\partial_t \\left(|u|^{q-1}u \\right) -\\operatorname{div} \\left( |Du|^{p-2} Du \\right) = \\operatorname{div} \\left( |F|^{p-2} F \\right) \\quad \\text{ in } \\Omega_T := \\Omega \\times (0,T) $$ with parameters $p>1$ and $q>0$ and $\\Omega\\subset\\mathbb{R}^n$. In this paper, we are concerned with the ranges $q>1$ and $p>\\frac{n(q+1)}{n+q+1}$. A key ingredient in the proof is an intrinsic geometry that takes both the solution $u$ and its spatial gradient $Du$ into account.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-07T11:10:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35K40",
      "35K55"
    ],
    "keywords": [
      "singular doubly nonlinear systems",
      "spatial gradient",
      "local higher integrability result",
      "doubly nonlinear parabolic systems",
      "weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}