{
  "id": "1404.0913",
  "version": "v1",
  "published": "2014-04-03T14:05:18.000Z",
  "updated": "2014-04-03T14:05:18.000Z",
  "title": "Lp-gradient harmonic maps into spheres and SO(N)",
  "authors": [
    "Armin Schikorra"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider critical points of the energy $E(v) := \\int_{\\mathbb{R}^n} |\\nabla^s v|^{\\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$, and $\\nabla^s = (\\partial_1^s,\\ldots,\\partial_n^s)$ is the formal fractional gradient, i.e. $\\partial_\\alpha^s$ is a composition of the fractional laplacian with the $\\alpha$-th Riesz transform. We show that critical points of this energy are H\\\"older continuous. As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which is interesting on its own.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T14:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "35B65",
      "35J60",
      "35S05"
    ],
    "keywords": [
      "lp-gradient harmonic maps",
      "formal fractional gradient",
      "critical points",
      "th riesz transform",
      "strzeleckis regularity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0913S"
    }
  }
}