{
  "id": "2306.14829",
  "version": "v1",
  "published": "2023-06-26T16:35:55.000Z",
  "updated": "2023-06-26T16:35:55.000Z",
  "title": "Nonlinear spectral problem for Hörmander vector fields",
  "authors": [
    "Mukhtar Karazym",
    "Durvudkhan Suragan"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Based on variational methods, we study a nonlinear eigenvalue problem for a $p$-sub-Laplacian type quasilinear operator arising from smooth H\\\"ormander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction and show H\\\"older regularity of eigenfunctions. Moreover, we determine the best constant for the $L^{p}$-Poincar\\'e inequality as a byproduct.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-26T16:35:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P30",
      "35A15",
      "53C17"
    ],
    "keywords": [
      "hörmander vector fields",
      "nonlinear spectral problem",
      "nonlinear eigenvalue problem",
      "sub-laplacian type quasilinear operator arising",
      "variational methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}