{
  "id": "1008.1939",
  "version": "v1",
  "published": "2010-08-11T15:34:49.000Z",
  "updated": "2010-08-11T15:34:49.000Z",
  "title": "A weak-strong convergence property and symmetry of minimizers of constrained variational problems in $\\mathbb{R}^N$",
  "authors": [
    "Hichem Hajaiej",
    "Stefan Krömer"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a weak-strong convergence result for functionals of the form $\\int_{\\mathbb{R}^N} j(x, u, Du)\\,dx$ on $W^{1,p}$, along equiintegrable sequences. We will then use it to study cases of equality in the extended Polya-Szeg\\\"o inequality and discuss applications of such a result to prove the symmetry of minimizers of a class of variational problems including nonlocal terms under multiple constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-11T15:34:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J50",
      "35B05",
      "49J45"
    ],
    "keywords": [
      "weak-strong convergence property",
      "constrained variational problems",
      "minimizers",
      "weak-strong convergence result",
      "study cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1939H"
    }
  }
}