{
  "id": "2404.00609",
  "version": "v1",
  "published": "2024-03-31T08:49:33.000Z",
  "updated": "2024-03-31T08:49:33.000Z",
  "title": "Strong maximum principle for generalized solutions to equations of the Monge-Ampère type",
  "authors": [
    "Huaiyu Jian",
    "Xushan Tu"
  ],
  "comment": "Strong maximum principle, Monge-Amp\\`ere equation, Strict convexity, Uniqueness",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Amp\\`ere type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily $C^{1,1}$ smooth, and show that it fails at non-strictly convex points. The results we obtain can be applied to various Minkowski type problems in convex geometry by the virtue of the Gauss image map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-31T08:49:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B50",
      "35J96"
    ],
    "keywords": [
      "generalized solutions",
      "monge-ampère type",
      "strong maximum principle holds",
      "minkowski type problems",
      "gauss image map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}