{
  "id": "2003.07265",
  "version": "v1",
  "published": "2020-03-16T15:03:33.000Z",
  "updated": "2020-03-16T15:03:33.000Z",
  "title": "Solvability In Weighted Lebesgue Spaces of the Divergence Equation with Measure Data",
  "authors": [
    "Laurent Moonens",
    "Emmanuel Russ"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "In the following paper, one studies, given a bounded, connected open set $\\Omega$ $\\subseteq$ R n , $\\kappa$ > 0, a positive Radon measure $\\mu$ 0 in $\\Omega$ and a (signed) Radon measure $\\mu$ on $\\Omega$ satisfying $\\mu$($\\Omega$) = 0 and |$\\mu$| $\\kappa$$\\mu$ 0 , the possibility of solving the equation div u = $\\mu$ by a vector field u satisfying |u| $\\kappa$w on $\\Omega$ (where w is an integrable weight only related to the geometry of $\\Omega$ and to $\\mu$ 0), together with a mild boundary condition. This extends results obtained in [4] for the equation div u = f , improving them on two aspects: one works here with the divergence equation with measure data, and also construct a weight w that relies in a softer way on the geometry of $\\Omega$, improving its behavior (and hence the a priori behavior of the solution we construct) substantially in some instances. The method used in this paper follows a constructive approach of Bogovskii type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-16T15:03:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted lebesgue spaces",
      "divergence equation",
      "measure data",
      "solvability",
      "bogovskii type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}