{
  "id": "1708.05648",
  "version": "v1",
  "published": "2017-08-18T15:27:14.000Z",
  "updated": "2017-08-18T15:27:14.000Z",
  "title": "Convex functional and the stratification of the singular set of their stationary points",
  "authors": [
    "Zahra Sinaei"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove partial regularity of stationary solutions and minimizers $u$ from a set $\\Omega\\subset \\mathbb R^n$ to a Riemannian manifold $N$, for the functional $\\int_\\Omega F(x,u,|\\nabla u|^2) dx$. The integrand $F$ is convex and satisfies some ellipticity and boundedness assumptions. We also develop a new monotonicity formula and an $\\epsilon$-regularity theorem for such stationary solutions with no restriction on their images. We then use the idea of quantitative stratification to show that the k-th strata of the singular set of such solutions are k-rectifiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-18T15:27:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular set",
      "stationary points",
      "convex functional",
      "stratification",
      "stationary solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}