{
  "id": "1911.04884",
  "version": "v1",
  "published": "2019-11-12T14:30:33.000Z",
  "updated": "2019-11-12T14:30:33.000Z",
  "title": "Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces",
  "authors": [
    "Felix Hummel",
    "Nick Lindemulder"
  ],
  "comment": "62 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted $L_{q}$-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt $A_{\\infty}$-class. In Besov space case we have the restriction that the microscopic parameter equals to $q$. Going beyond the $A_{p}$-range, where $p$ is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-12T14:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K52",
      "46E35",
      "46E40",
      "47G30"
    ],
    "keywords": [
      "parabolic boundary value problems",
      "weighted function spaces",
      "triebel-lizorkin space",
      "extra flexibility",
      "treat rougher boundary data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}