{
  "id": "2408.07528",
  "version": "v1",
  "published": "2024-08-14T13:02:34.000Z",
  "updated": "2024-08-14T13:02:34.000Z",
  "title": "Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value",
  "authors": [
    "Nguyen Van Phu",
    "Nguyen Quang Dieu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP",
    "math.CV"
  ],
  "abstract": "In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-\\chi(u)H_{m}(u)=\\mu$ in the class $\\mathcal{E}_{m,\\chi}(f,\\Omega)$ if there exists subsolution in this class, where the given boundary value $f\\in\\mathcal{N}_m(\\Omega)\\cap MSH_m(\\Omega).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T13:02:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32U05",
      "32W20"
    ],
    "keywords": [
      "hessian type equation",
      "weighted energy classes",
      "boundary value",
      "subharmonic functions",
      "subsolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}