{
  "id": "0908.1509",
  "version": "v2",
  "published": "2009-08-11T19:48:29.000Z",
  "updated": "2012-09-26T09:15:50.000Z",
  "title": "Sharp heat kernel estimates for relativistic stable processes in open sets",
  "authors": [
    "Zhen-Qing Chen",
    "Panki Kim",
    "Renming Song"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP611 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2012, Vol. 40, No. 1, 213-244",
  "doi": "10.1214/10-AOP611",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators $m-(m^{2/\\alpha}-\\Delta)^{\\alpha/2}$] in $C^{1,1}$ open sets. Here $m>0$ and $\\alpha\\in(0,2)$. The estimates are uniform in $m\\in(0,M]$ for each fixed $M>0$. Letting $m\\downarrow0$, we recover the Dirichlet heat kernel estimates for $\\Delta^{\\alpha/2}:=-(-\\Delta)^{\\alpha/2}$ in $C^{1,1}$ open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded $C^{1,1}$ open sets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-26T09:15:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relativistic stable processes",
      "sharp heat kernel estimates",
      "open sets",
      "dirichlet heat kernel estimates",
      "establish sharp two-sided estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.1509C"
    }
  }
}