{
  "id": "2002.01383",
  "version": "v1",
  "published": "2020-02-04T16:06:30.000Z",
  "updated": "2020-02-04T16:06:30.000Z",
  "title": "Maximal $L^p$-regularity for a Class of Integro-Differential Equations",
  "authors": [
    "A. Amansag",
    "H. Bounit",
    "A. Driouich",
    "S. Hadd"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We propose an approach based on perturbation theory to establish maximal $L^p$-regularity for a class of integro-differential equations. As the left shift semigroup is involved for such equations, we study maximal regularity on Bergman spaces for autonomous and non-autonomous integro-differential equations. Our method is based on the formulation of the integro-differential equations to a Cauchy problems, infinite dimensional systems theory and some recent results on the perturbation of maximal regularity (see \\cite{AmBoDrHa}). Applications to heat equations driven by the Dirichlet (or Neumann)-Laplacian are considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-04T16:06:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "35B65",
      "32A36"
    ],
    "keywords": [
      "infinite dimensional systems theory",
      "study maximal regularity",
      "left shift semigroup",
      "heat equations driven",
      "cauchy problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}