{
  "id": "1205.1089",
  "version": "v1",
  "published": "2012-05-05T01:42:14.000Z",
  "updated": "2012-05-05T01:42:14.000Z",
  "title": "The Green function for elliptic systems in two dimensions",
  "authors": [
    "J. L. Taylor",
    "S. Kim",
    "R. M. Brown"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. We consider the elliptic system in a Lipschitz domain with mixed boundary conditions. Thus we specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We require a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary conditions. Our proof proceeds by defining a variant of the space $BMO(\\partial \\Omega)$ that is adapted to the boundary conditions and showing that the solution exists in this space. We also give a construction of the Green function with Neumann boundary conditions and the fundamental solution in the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-05T01:42:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "green function",
      "dimensions",
      "fundamental solution",
      "divergence form elliptic system",
      "specify dirichlet boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1089T"
    }
  }
}