{
  "id": "2110.04377",
  "version": "v3",
  "published": "2021-10-08T20:58:07.000Z",
  "updated": "2022-05-05T18:57:04.000Z",
  "title": "Regularity of quasi-linear equations with Hörmander vector fields of step two",
  "authors": [
    "Giovanna Citti",
    "Shirsho Mukherjee"
  ],
  "comment": "46 pages, additions and corrections made",
  "categories": [
    "math.AP"
  ],
  "abstract": "If the smooth vector fields $X_1,\\ldots,X_m$ and their commutators span the tangent space at every point in $\\Omega\\subseteq \\mathbb{R}^N$ for any fixed $m\\leq N$, then we establish the full interior regularity theory of quasi-linear equations $\\sum_{i=1}^m X_i^*A_i(X_1u, \\ldots,X_mu)= 0$ with $p$-Laplacian type growth condition. In other words, we show that a weak solution of the equation is locally $C^{1,\\alpha}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-05-05T18:57:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H20",
      "35J92",
      "35B65"
    ],
    "keywords": [
      "hörmander vector fields",
      "quasi-linear equations",
      "laplacian type growth condition",
      "full interior regularity theory",
      "smooth vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}