{
  "id": "2006.07636",
  "version": "v1",
  "published": "2020-06-13T13:09:25.000Z",
  "updated": "2020-06-13T13:09:25.000Z",
  "title": "Energy estimates of harmonic maps between Riemannian manifolds",
  "authors": [
    "M. A. Ragusa",
    "A. Tachikawa"
  ],
  "categories": [
    "math.AP",
    "math.CT"
  ],
  "abstract": "Let $\\Omega \\subset {R}^n,$ $n \\geq 3,$ be a bounded open set, $x=(x_1,x_2,\\ldots,x_n)$ a generic point which belongs to $\\Omega,$ $u \\colon \\Omega \\to {R}^N ,$ $N>1,$ and $ Du=(D_\\alpha u^i)$, $D_\\alpha = \\partial/\\partial x_\\alpha, $ $\\alpha =1,\\ldots,n,\\,$ $i=1,\\ldots,N .\\,$ Main goal is the study of regularity of the minima of nondifferentiable functionals $$ {\\cal F} \\,=\\, \\int_\\Omega F(x,u,Du) dx. $$ having the integrand function different shapes of smoothness. The method is based on the use some majorizations for the functional, rather than the well known Euler equation associated to it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-13T13:09:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic maps",
      "riemannian manifolds",
      "energy estimates",
      "generic point",
      "euler equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}