{
  "id": "0901.4127",
  "version": "v1",
  "published": "2009-01-26T21:44:38.000Z",
  "updated": "2009-01-26T21:44:38.000Z",
  "title": "Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part",
  "authors": [
    "Mohammud Foondun"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Dirichlet form given by \\sE(f,f)&=&{1/2}\\int_{\\bR^d}\\sum_{i,j=1}^d a_{ij}(x)\\frac{\\partial f(x)}{\\partial x_i} \\frac{\\partial f(x)}{\\partial x_j} dx &+&\\int_{\\bR^d\\times \\bR^d} (f(y)-f(x))^2J(x,y)dxdy. Under the assumption that the $\\{a_{ij}\\}$ are symmetric and uniformly elliptic and with suitable conditions on $J$, the nonlocal part, we obtain upper and lower bounds on the heat kernel of the Dirichlet form. We also prove a Harnack inequality and a regularity theorem for functions that are harmonic with respect to $\\sE$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-26T21:44:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "60J75"
    ],
    "keywords": [
      "heat kernel estimates",
      "dirichlet form",
      "harnack inequality",
      "non-local part",
      "nonlocal part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}