{
  "id": "2003.04554",
  "version": "v1",
  "published": "2020-03-10T06:54:52.000Z",
  "updated": "2020-03-10T06:54:52.000Z",
  "title": "An introduction to maximal regularity for parabolic evolution equations",
  "authors": [
    "Robert Denk"
  ],
  "comment": "57 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we give an introduction to the concept of maximal $L^p$-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and $\\mathcal R$-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-10T06:54:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35-02",
      "35K90",
      "42B35",
      "35B65"
    ],
    "keywords": [
      "parabolic evolution equations",
      "general parabolic boundary value problems",
      "introduction",
      "first define maximal regularity",
      "nonlinear partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}