{
  "id": "2407.20022",
  "version": "v1",
  "published": "2024-07-29T14:01:13.000Z",
  "updated": "2024-07-29T14:01:13.000Z",
  "title": "Regularity theory for fully nonlinear equations of porous medium-type",
  "authors": [
    "Hyungsung Yun"
  ],
  "comment": "24 pages. arXiv admin note: text overlap with arXiv:2305.14615",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global $C^{2,\\alpha}$-estimates of viscosity solutions. In many PDE problems, the $C^{2,\\alpha}$-estimates have been obtained through Schauder-type estimates. However, the Schauder-type estimates are not applicable to the porous medium-type equations. We provide techniques for handling porous medium-type equations so that the global $C^{2,\\alpha}$-estimates can be established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T14:01:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35D40",
      "35K55",
      "35K65"
    ],
    "keywords": [
      "fully nonlinear equations",
      "regularity theory",
      "schauder-type estimates",
      "zero dirichlet boundary condition",
      "pde problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}