{
  "id": "2406.03297",
  "version": "v1",
  "published": "2024-06-05T14:07:38.000Z",
  "updated": "2024-06-05T14:07:38.000Z",
  "title": "Functional calculus on weighted Sobolev spaces for the Laplacian on the half-space",
  "authors": [
    "Nick Lindemulder",
    "Emiel Lorist",
    "Floris Roodenburg",
    "Mark Veraar"
  ],
  "comment": "50 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Laplace operator on the half-space with Dirichlet and Neumann boundary conditions. We prove that this operator admits a bounded $H^\\infty$-calculus on Sobolev spaces with power weights measuring the distance to the boundary. These weights do not necessarily belong to the class of Muckenhoupt $A_p$ weights. We additionally study the corresponding Dirichlet and Neumann heat semigroup. It is shown that these semigroups, in contrast to the $L^p$-case, have polynomial growth. Moreover, maximal regularity results for the heat equation are derived on inhomogeneous and homogeneous weighted Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T14:07:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "35K20",
      "46E35",
      "47D03"
    ],
    "keywords": [
      "functional calculus",
      "half-space",
      "maximal regularity results",
      "neumann boundary conditions",
      "neumann heat semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}