{
  "id": "1006.1455",
  "version": "v1",
  "published": "2010-06-08T05:32:45.000Z",
  "updated": "2010-06-08T05:32:45.000Z",
  "title": "Viscosity solutions to second order parabolic PDEs on Riemannian manifolds",
  "authors": [
    "Xuehong Zhu"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we consider viscosity solutions to second order parabolic PDEs $u_{t}+F(t,x,u,du,d^{2}u)=0$ defined on compact Riemannian manifolds with boundary conditions. We prove comparison, uniqueness and existence results for the solutions. Under the assumption that the manifold $M$ has nonnegative sectional curvature, we get the finest results. If one additionally requires $F$ to depend on $d^{2}u$ in a uniformly continuous manner, the assumptions on curvature can be thrown away.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-08T05:32:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J52",
      "49L25",
      "35D05"
    ],
    "keywords": [
      "second order parabolic pdes",
      "viscosity solutions",
      "compact riemannian manifolds",
      "existence results",
      "assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1455Z"
    }
  }
}