{
  "id": "2308.11383",
  "version": "v1",
  "published": "2023-08-22T12:19:19.000Z",
  "updated": "2023-08-22T12:19:19.000Z",
  "title": "Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels",
  "authors": [
    "Xavier Fernández-Real",
    "Xavier Ros-Oton"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study integro-differential elliptic equations (of order $2s$) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this setting, both in divergence and non-divergence form. Furthermore, we also establish H\\\"older estimates for general elliptic equations with no regularity assumption on $x$, including for the first time operators like $\\sum_{i=1}^n(-\\partial^2_{\\textbf{v}_i(x)})^s$, provided that the coefficients have ``small oscillation''.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-22T12:19:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35R11",
      "47G20"
    ],
    "keywords": [
      "nonlocal elliptic equations",
      "cordes-nirenberg estimates",
      "singular kernels",
      "study integro-differential elliptic equations",
      "first time operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}