{
  "id": "1105.4073",
  "version": "v1",
  "published": "2011-05-20T12:40:44.000Z",
  "updated": "2011-05-20T12:40:44.000Z",
  "title": "Hodge-Helmholtz Decompositions of Weighted Sobolev Spaces in Irregular Exterior Domains with Inhomogeneous and Anisotropic Media",
  "authors": [
    "Dirk Pauly"
  ],
  "comment": "Key Words: Hodge-Helmholtz decompositions, Maxwell's equations, electro-magnetic theory, weighted Sobolev spaces",
  "journal": "Mathematical Methods in the Applied Sciences, 31, (2008), 1509-1543",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, in electro-magnetic theory for exterior domains. In the appendix we translate our results to the classical framework of vector analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-20T12:40:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q60",
      "58A10",
      "58A14",
      "78A25",
      "78A30"
    ],
    "keywords": [
      "weighted sobolev spaces",
      "irregular exterior domains",
      "anisotropic media",
      "hodge-helmholtz decompositions",
      "inhomogeneous"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1002/mma.982",
      "journal": "Mathematical Methods in the Applied Sciences",
      "year": 2008,
      "month": "Sep",
      "volume": 31,
      "number": 13,
      "pages": 1509
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008MMAS...31.1509P"
    }
  }
}