{
  "id": "1403.2133",
  "version": "v2",
  "published": "2014-03-10T03:10:13.000Z",
  "updated": "2018-08-29T05:01:06.000Z",
  "title": "The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds",
  "authors": [
    "Bo Guan"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We solve the Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds under essentially optimal structure conditions, especially with no restrictions to the curvature of the underlying manifold and the second fundamental form of its boundary. The main result (Theorem 1.1) includes a new (and optimal) result in the Euclidean case. We introduce some new ideas and methods in deriving a priori estimates, which can be used to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-10T03:10:13.000Z",
      "abstract": "We study a class of fully nonlinear elliptic equations on Riemannian manifolds and solve the Dirichlet problem in a domain with no geometric restrictions to the boundary under essentially optimal structure conditions. It includes a new (and optimal) result in the Euclidean case. We introduce some new methods in deriving a priori second order estimates, which can be used to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-08-29T05:01:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "58J05",
      "35B45"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "riemannian manifolds",
      "dirichlet problem",
      "priori second order estimates",
      "essentially optimal structure conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2133G"
    }
  }
}