{
  "id": "1707.02816",
  "version": "v1",
  "published": "2017-07-10T12:06:48.000Z",
  "updated": "2017-07-10T12:06:48.000Z",
  "title": "On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations",
  "authors": [
    "Vladimir Bobkov",
    "Sergei Kolonitskii"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation $-\\Delta_p u = f(u)$ in bounded Steiner symmetric domains $\\Omega \\subset \\mathbb{R}^N$ under the zero Dirichlet boundary conditions. The nonlinearity $f$ is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet $p$-Laplacian in $\\Omega$. We show that the nodal set of any least energy sign-changing solution intersects the boundary of $\\Omega$. The proof is based on a moving polarization argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-10T12:06:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35B06",
      "49K30"
    ],
    "keywords": [
      "nodal set",
      "quasilinear elliptic equations",
      "zero dirichlet boundary conditions",
      "bounded steiner symmetric domains",
      "energy sign-changing solution intersects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}