{
  "id": "2307.13456",
  "version": "v1",
  "published": "2023-07-25T12:37:09.000Z",
  "updated": "2023-07-25T12:37:09.000Z",
  "title": "Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces",
  "authors": [
    "Wojciech Górny"
  ],
  "comment": "29 pages. arXiv admin note: text overlap with arXiv:2103.13373",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-25T12:37:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J52",
      "58J35",
      "35K90",
      "35K92"
    ],
    "keywords": [
      "gradient flow",
      "weak solutions",
      "inhomogeneous growth",
      "metric spaces",
      "functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}