{
  "id": "2001.00676",
  "version": "v1",
  "published": "2020-01-03T01:21:13.000Z",
  "updated": "2020-01-03T01:21:13.000Z",
  "title": "On Neumann problems for elliptic and parabolic equations on bounded manifolds",
  "authors": [
    "Sheng Guo"
  ],
  "comment": "45 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study fully nonlinear second-order elliptic and parabolic equations with Neumann boundary conditions on compact Riemannian manifolds with smooth boundary. We derive oscillation bounds for admissible solutions with Neumann boundary condition $u_\\nu = \\phi(x)$ assuming the existence of suitable $\\mathcal{C}$-subsolutions. We use a parabolic approach to derive a solution of a $k$-Hessian equation with Neumann boundary condition $u_\\nu = \\phi(x)$ under suitable assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-03T01:21:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35B45",
      "35J25",
      "35K10",
      "35K20",
      "35K20",
      "58J05",
      "58J32",
      "58J35"
    ],
    "keywords": [
      "parabolic equations",
      "neumann boundary condition",
      "neumann problems",
      "bounded manifolds",
      "study fully nonlinear second-order elliptic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}