{
  "id": "2005.02584",
  "version": "v1",
  "published": "2020-05-06T03:49:30.000Z",
  "updated": "2020-05-06T03:49:30.000Z",
  "title": "Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders",
  "authors": [
    "Minhyun Kim",
    "Ki-Ahm Lee"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to the fractional Laplacian type operators having a fixed order of differentiability $\\sigma \\in (0,2)$, the operators under consideration have variable orders of differentiability. Since the order is not characterized by a single number, we consider a function $\\varphi$ describing the variable orders of differentiability, which is allowed to oscillate between two functions $r^{\\sigma_1}$ and $r^{\\sigma_2}$ for some $0 < \\sigma_1 \\leq \\sigma_2 < 2$. By introducing the generalized H\\\"older spaces, we provide $C^{\\varphi\\psi}$ estimates that generalizes the standard Evans--Krylov and Schauder type $C^{\\sigma+\\alpha}$ estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-06T03:49:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schauder type estimates",
      "nonlocal fully nonlinear equations",
      "variable orders",
      "rough kernels",
      "generalized evans-krylov"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}