{
  "id": "2106.07637",
  "version": "v1",
  "published": "2021-06-14T17:53:03.000Z",
  "updated": "2021-06-14T17:53:03.000Z",
  "title": "On a class of divergence form linear parabolic equations with degenerate coefficients",
  "authors": [
    "Tuoc Phan",
    "Hung Vinh Tran"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-\\infty, T) \\times \\mathbb{R}^d_+$, where $\\mathbb{R}^d_+ = \\{x \\in \\mathbb{R}^d\\,:\\, x_d>0\\}$ and $T\\in {(-\\infty, \\infty]}$ is given, and the diffusion matrices are the product of $x_d$ and bounded uniformly elliptic matrices, which are degenerate at $\\{x_d=0\\}$. As such, our class of equations resembles well the corresponding class of degenerate viscous Hamilton-Jacobi equations. We obtain wellposedness results and regularity type estimates in some appropriate weighted Sobolev spaces for the solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-14T17:53:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divergence form linear parabolic equations",
      "degenerate coefficients",
      "upper half space",
      "appropriate weighted sobolev spaces",
      "regularity type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}