{
  "id": "2401.07880",
  "version": "v1",
  "published": "2024-01-15T18:17:28.000Z",
  "updated": "2024-01-15T18:17:28.000Z",
  "title": "Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost",
  "authors": [
    "Augusto Gerolin",
    "Mircea Petrache",
    "Adolfo Vargas-Jimenez"
  ],
  "comment": "19 pages, all comments welcome",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we introduce such dissociation model, the corresponding optimal transport problem as well as show preliminary results on the existence and uniqueness of Monge solutions assuming absolute continuity of at least two of the marginals. Finally, we show that such marginal regularity conditions are necessary for the existence of an unique Monge solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T18:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-marginal optimal transport problem",
      "intermolecular interactions cost",
      "monge minimizers",
      "solutions assuming absolute continuity",
      "optimal transport problem arising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}