{
  "id": "2410.20419",
  "version": "v1",
  "published": "2024-10-27T12:04:22.000Z",
  "updated": "2024-10-27T12:04:22.000Z",
  "title": "Estimates on the Laplace Operator of Harmonic Maps",
  "authors": [
    "Qingtong Wu"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In this paper we investigate estimates about the Laplace operator of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain higher-order estimates. We consider the problem subject to the $\\mathbb{T}^2$ and $\\mathbb{T}^3$ boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T12:04:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic maps",
      "laplace operator",
      "general ericksen-leslie system",
      "higher-order estimates",
      "problem subject"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}