{
  "id": "2310.08297",
  "version": "v1",
  "published": "2023-10-12T13:01:41.000Z",
  "updated": "2023-10-12T13:01:41.000Z",
  "title": "Elliptic Equations in Divergence Form with Discontinuous Coefficients in Domains with Corners",
  "authors": [
    "Jun Chen",
    "Xuemei Deng"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the equations in divergence form with piecewise $C^{\\ga}$ coefficients. The domains contain corners and the discontinuity surfaces are attached to edges of the corners. We obtain piecewise $C^{1,\\ga}$ estimates across the discontinuity surfaces and provide an example to illustrate the issue about the regularity at the corners.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T13:01:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divergence form",
      "elliptic equations",
      "discontinuous coefficients",
      "discontinuity surfaces",
      "domains contain corners"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}