{
  "id": "2106.03448",
  "version": "v1",
  "published": "2021-06-07T09:25:08.000Z",
  "updated": "2021-06-07T09:25:08.000Z",
  "title": "Hilbert Complexes with Mixed Boundary Conditions: Regular Decompositions, Compact Embeddings, and Functional Analysis ToolBox -- Part 1: De Rham Complex",
  "authors": [
    "Dirk Pauly",
    "Michael Schomburg"
  ],
  "comment": "Key Words: regular potentials, regular decompositions, compact embeddings, Hilbert complexes, Mixed Boundary Conditions, de Rham complex",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.KT",
    "math.MP"
  ],
  "abstract": "We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis together with particular regular decompositions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-07T09:25:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mixed boundary conditions",
      "functional analysis toolbox",
      "regular decompositions",
      "compact embeddings",
      "rham complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}