{
  "id": "math/0612742",
  "version": "v3",
  "published": "2006-12-23T13:30:58.000Z",
  "updated": "2008-03-13T00:11:04.000Z",
  "title": "Viscosity solutions to second order partial differential equations on Riemannian manifolds",
  "authors": [
    "Daniel Azagra",
    "Juan Ferrera",
    "Beatriz Sanz"
  ],
  "comment": "Final version: the domain of F in the equation F=0 has been changed in order to get more generality and simplicity in the definitions and assumptions, and several important misprints have been corrected",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations $F(x, u, du, d^{2}u)=0$ defined on a finite-dimensional Riemannian manifold $M$. Finest results (with hypothesis that require the function $F$ to be degenerate elliptic, that is nonincreasing in the second order derivative variable, and uniformly continuous with respect to the variable $x$) are obtained under the assumption that $M$ has nonnegative sectional curvature, while, if one additionally requires $F$ to depend on $d^{2}u$ in a uniformly continuous manner, then comparison results are established with no restrictive assumptions on curvature.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-03-13T00:11:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J32",
      "49J52",
      "49L25",
      "35D05",
      "35J70"
    ],
    "keywords": [
      "second order partial differential equations",
      "riemannian manifold",
      "viscosity solutions",
      "nonlinear second order partial differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12742A"
    }
  }
}