{
  "id": "2303.15843",
  "version": "v1",
  "published": "2023-03-28T09:31:48.000Z",
  "updated": "2023-03-28T09:31:48.000Z",
  "title": "Isoperimetric inequalities and regularity of $A$-harmonic functions on surfaces",
  "authors": [
    "Tomasz Adamowicz",
    "Giona Veronelli"
  ],
  "comment": "27 pg",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We investigate the logarithmic and power-type convexity of the length of the level curves for $a$-harmonic functions on smooth surfaces and related isoperimetric inequalities. In particular, our analysis covers the $p$-harmonic and the minimal surface equations. As an auxiliary result, we obtain higher Sobolev regularity properties of the solutions, including the $W^{2,2}$ regularity. The results are complemented by a number of estimates for the derivatives $L'$ and $L''$ of the length of the level curve function $L$, as well as by examples illustrating the presentation. Our work generalizes results due to Alessandrini, Longinetti, Talenti and Lewis in the Euclidean setting, as well as a recent article of ours devoted to the harmonic case on surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T09:31:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R01",
      "58E20",
      "31C12",
      "53C21"
    ],
    "keywords": [
      "harmonic functions",
      "higher sobolev regularity properties",
      "level curve function",
      "work generalizes results",
      "minimal surface equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}