{
  "id": "1904.08856",
  "version": "v1",
  "published": "2019-04-18T15:56:45.000Z",
  "updated": "2019-04-18T15:56:45.000Z",
  "title": "Geometric regularity for elliptic equations in double-divergence form",
  "authors": [
    "Raimundo Leitão",
    "Edgard A. Pimentel",
    "Makson S. Santos"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\\\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\\alpha$-H\\\"older continuous coefficients lead to solutions of class $\\mathcal{C}^{1^-}$, locally. Under the assumption of Sobolev differentiable coefficients, we establish regularity in the class $\\mathcal{C}^{1,1^-}$. Our results unveil improved continuity along a nonphysical free boundary, where the weak formulation of the problem vanishes. We argue through a geometric set of techniques, implemented by approximation methods. Such methods connect our problem of interest with a target profile. An iteration procedure imports information from this limiting configuration to the solutions of the double-divergence equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-18T15:56:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J15"
    ],
    "keywords": [
      "elliptic equations",
      "double-divergence form",
      "geometric regularity",
      "double-divergence equation",
      "iteration procedure imports information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}