{
  "id": "2409.14102",
  "version": "v1",
  "published": "2024-09-21T10:54:05.000Z",
  "updated": "2024-09-21T10:54:05.000Z",
  "title": "On some interpolation inequalities between Hölder and Lebesgue's spaces",
  "authors": [
    "Sergey P. Degtyarev"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We present a simple proof of some interpolation inequalities between H\\\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate in a smooth H\\\"{o}lder class for a solution to some quasilinear parabolic initial boundary value problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-21T10:54:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "35K59"
    ],
    "keywords": [
      "interpolation inequalities",
      "lebesgues spaces",
      "parabolic initial boundary value problem",
      "quasilinear parabolic initial boundary value",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}