{
  "id": "2405.11925",
  "version": "v1",
  "published": "2024-05-20T10:03:26.000Z",
  "updated": "2024-05-20T10:03:26.000Z",
  "title": "The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds",
  "authors": [
    "Weisong Dong",
    "Jinling Niu",
    "Nadilamu Nizhamuding"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the Dirichlet problem for Monge-Amp\\`ere type equations for $p$-plurisubharmonic functions on Riemannian manifolds. The $a$ $priori$ estimates up to the second order derivatives of solutions are established. The existence of a solution then follows by the continuity method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-20T10:03:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35B45"
    ],
    "keywords": [
      "monge-ampère type equations",
      "riemannian manifolds",
      "dirichlet problem",
      "second order derivatives",
      "plurisubharmonic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}