{
  "id": "2307.01654",
  "version": "v1",
  "published": "2023-07-04T11:23:19.000Z",
  "updated": "2023-07-04T11:23:19.000Z",
  "title": "Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients",
  "authors": [
    "Sun-Sig Byun",
    "Kyeongbae Kim",
    "Deepak Kumar"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove Calder\\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of fractional Laplacian type data and a non-divergence type data. Interestingly, even though the kernel coefficients are discontinuous, we obtain a significant increment of fractional differentiability for the solutions, which is not observed in the corresponding local parabolic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-04T11:23:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calderón-zygmund theory",
      "discontinuous coefficients",
      "fractional laplacian type data",
      "kernel coefficients",
      "calderon-zygmund type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}