{
  "id": "1302.7062",
  "version": "v2",
  "published": "2013-02-28T02:52:49.000Z",
  "updated": "2013-11-25T20:38:35.000Z",
  "title": "Interior regularity of fully nonlinear degenerate elliptic equations, I: Bellman equations with constant coefficients",
  "authors": [
    "Wei Zhou"
  ],
  "comment": "Assumption 2.2 was corrected and then weakened. The original Assumption 2.2 after correction is now Remark 2.1. Minor revision was made accordingly on pages 28 and 29. A few typos were corrected also",
  "categories": [
    "math.AP",
    "math.OC",
    "math.PR"
  ],
  "abstract": "This is the first of a series of papers on the interior regularity of fully nonlinear degenerate elliptic equations. We consider a stochastic optimal control problem in which the diffusion coefficients, drift coefficients and discount factor are independent of the spacial variables. Under suitable assumptions, for $k=0,1$, when the terminal and running payoffs are globally $C^{k,1}$, we obtain the $C^{k,1}$-smoothness of the value function, which yields the existence and uniqueness of the solution to the associated Dirichlet problem for the degenerate Bellman equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-25T20:38:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J60",
      "35J70",
      "60H30",
      "93E20"
    ],
    "keywords": [
      "fully nonlinear degenerate elliptic equations",
      "interior regularity",
      "constant coefficients",
      "stochastic optimal control problem",
      "degenerate bellman equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7062Z"
    }
  }
}