{
  "id": "math/0105044",
  "version": "v4",
  "published": "2001-05-05T21:04:40.000Z",
  "updated": "2001-11-05T16:09:00.000Z",
  "title": "Majorisation with applications to the calculus of variations",
  "authors": [
    "Marius Buliga"
  ],
  "comment": "13 pages",
  "journal": "appeared as \"Four applications of majorization to convexity in the calculus of variations\", Linear Algebra and its Applications, Volume 429, Issue 7, 1 October 2008, Pages 1528-1545",
  "doi": "10.1016/j.laa.2008.04.023",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of possible non-polyconvex but multiplicative quasiconvex isotropic functions. This class is not contained in a well known theorem of Ball (6.3 in this paper) which gives sufficient conditions for an isotropic and objective function to be polyconvex. We show here that there is a new way to prove directly the quasiconvexity (in the multiplicative form). Relevance of Schur convexity for the description of rank one convex hulls is explained.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2001-11-05T16:09:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74A20",
      "14A42"
    ],
    "keywords": [
      "majorisation",
      "variations",
      "applications",
      "sufficient conditions",
      "schur convexity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5044B"
    }
  }
}