{
  "id": "1709.02329",
  "version": "v1",
  "published": "2017-09-07T16:10:31.000Z",
  "updated": "2017-09-07T16:10:31.000Z",
  "title": "On regularity theory for n/p-harmonic maps into manifolds",
  "authors": [
    "Francesca Da Lio",
    "Armin Schikorra"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we continue the investigation of the regularity of the so-called weak $\\frac{n}{p}$-harmonic maps in the critical case. These are critical points of the following nonlocal energy \\[ {\\mathcal{L}}_s(u)=\\int_{\\mathbb{R}^n}| ( {-\\Delta})^{\\frac{s}{2}} u(x)|^p dx\\,, \\] where $u\\in \\dot{H}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ and ${\\mathcal{N}}\\subset\\mathbb{R}^N$ is a closed $k$ dimensional smooth manifold and $s=\\frac{n}{p}$. We prove H\\\"older continuity for such critical points for $p \\leq 2$. For $p > 2$ we obtain the same under an additional Lorentz-space assumption. The regularity theory is in the two cases based on regularity results for nonlocal Schr\\\"odinger systems with an antisymmetric potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-07T16:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "35J20",
      "35B65",
      "35J60",
      "35S99"
    ],
    "keywords": [
      "regularity theory",
      "n/p-harmonic maps",
      "critical points",
      "dimensional smooth manifold",
      "additional lorentz-space assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}