{
  "id": "2403.06791",
  "version": "v1",
  "published": "2024-03-11T15:08:34.000Z",
  "updated": "2024-03-11T15:08:34.000Z",
  "title": "Dirichlet heat kernel estimates of subordinate diffusions with continuous components in $C^{1, α}$ open sets",
  "authors": [
    "Jie-Ming Wang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels for a class of subordinate diffusions with continuous components when the scaling order of purely discontinuous part of the subordinator is between $0$ and $1$ including $1$ in $C^{1, \\alpha}(\\alpha\\in (0, 1])$ open sets. As a corollary, we obtain the sharp two-sided estimates for Green functions of these processes in bounded $C^{1, \\alpha}$ open sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-11T15:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet heat kernel estimates",
      "open sets",
      "subordinate diffusions",
      "continuous components",
      "derive explicit sharp two-sided estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}