{
  "id": "1605.02340",
  "version": "v1",
  "published": "2016-05-08T17:28:53.000Z",
  "updated": "2016-05-08T17:28:53.000Z",
  "title": "Convex integration with linear constraints and its applications",
  "authors": [
    "Seonghak Kim"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study solutions of the first order partial differential inclusions of the form $\\nabla u\\in K$, where $u:\\Omega\\subset\\mathbb{R}^n\\to\\mathbb{R}^m$ and $K$ is a set of $m\\times n$ real matrices, and derive a companion version to the result of {M\\\"uller and \\v{S}ver\\'ak} [20], concerning a general linear constraint on the components of $\\nabla u$. We then consider two applications: the vectorial eikonal equation and a $T_4$-configuration both under linear constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-08T17:28:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F60",
      "35D30"
    ],
    "keywords": [
      "convex integration",
      "applications",
      "first order partial differential inclusions",
      "vectorial eikonal equation",
      "general linear constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}