{
  "id": "1805.10213",
  "version": "v1",
  "published": "2018-05-25T15:51:16.000Z",
  "updated": "2018-05-25T15:51:16.000Z",
  "title": "The heat equation with rough boundary conditions and holomorphic functional calculus",
  "authors": [
    "Nick Lindemulder",
    "Mark Veraar"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded $H^\\infty$-calculus on weighted $L^p$-spaces for power weights which fall outside the classical class of $A_p$-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with rough inhomogeneous boundary data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T15:51:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K50",
      "47A60",
      "46B70",
      "46E35",
      "46E40"
    ],
    "keywords": [
      "holomorphic functional calculus",
      "rough boundary conditions",
      "heat equation",
      "dirichlet boundary conditions",
      "maximal regularity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}