{
  "id": "math/0702743",
  "version": "v2",
  "published": "2007-02-25T10:08:12.000Z",
  "updated": "2007-11-17T19:44:05.000Z",
  "title": "Minimizers of Dirichlet functionals on the n-torus and the Weak KAM Theory",
  "authors": [
    "Gershon Wolansky"
  ],
  "comment": "35 pages, no figures",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "Given a probability measure $\\mu$ on the $n-$torus $T^n$ and a rotation vector $k\\in R^n$, we ask wether there exists a minimizer to the integral $\\int_{T^n} |\\grad\\phi+k|^2 d\\mu$. This problem leads, naturally, to a class of elliptic PDE and to an optimal transportation (Monge-Kantorovich) class of problems on the torus. It is also related to higher dimensional Aubry-Mather theory, dealing with invariant sets of periodic Lagrangians, and is known as the \"Weak-KAM theory\".",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-17T19:44:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K20",
      "65K10",
      "90C47"
    ],
    "keywords": [
      "weak kam theory",
      "dirichlet functionals",
      "higher dimensional aubry-mather theory",
      "rotation vector",
      "weak-kam theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2743W"
    }
  }
}