{
  "id": "1611.00281",
  "version": "v1",
  "published": "2016-11-01T15:54:19.000Z",
  "updated": "2016-11-01T15:54:19.000Z",
  "title": "Poincare inequality and well-posedness of the Poisson problem on manifolds with boundary and bounded geometry",
  "authors": [
    "Bernd Ammann",
    "Nadine Große",
    "Victor Nistor"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let M be a manifold with boundary and bounded geometry. We assume that M has \"finite width,\" that is, that the distance $dist(x, \\partial M)$ from any point $x \\in M$ to the boundary $\\partial M$ is bounded uniformly. Under this assumption, we prove that the Poincar\\'e inequality for vector valued functions holds on $M$. We also prove a general regularity result for uniformly strongly elliptic equations and systems on general manifolds with boundary and bounded geometry. By combining the Poincar\\'e inequality with the regularity result, we obtain---as in the classical case---that uniformly strongly elliptic equations and systems are well-posed on $M$ in Hadamard's sense between the usual Sobolev spaces associated to the metric. We also provide variants of these results that apply to suitable mixed Dirichlet-Neumann boundary conditions. We also indicate applications to boundary value problems on singular domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-01T15:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J67",
      "35J47",
      "35R01",
      "58J32"
    ],
    "keywords": [
      "poincare inequality",
      "bounded geometry",
      "uniformly strongly elliptic equations",
      "poisson problem",
      "mixed dirichlet-neumann boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}