{
  "id": "1406.0742",
  "version": "v1",
  "published": "2014-06-03T15:15:55.000Z",
  "updated": "2014-06-03T15:15:55.000Z",
  "title": "$C^0$-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators",
  "authors": [
    "Camelia A. Pop"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Kimura diffusions serve as a stochastic model for the evolution of gene frequencies in population genetics. Their infinitesimal generator is an elliptic differential operator whose second-order coefficients matrix degenerates on the boundary of the domain. In this article, we consider the inhomogeneous initial-value problem defined by generators of Kimura diffusions, and we establish $C^0$-estimates, which allows us to prove that solutions to the inhomogeneous initial-value problem are smooth up to the boundary of the domain where the operator degenerates, even when the initial data is only assumed to be continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-03T15:15:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic equation",
      "kimura operators",
      "inhomogeneous initial-value problem",
      "second-order coefficients matrix degenerates",
      "smoothness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.0742P"
    }
  }
}