English

On the Gibbons' conjecture for equations involving the $p$-Laplacian

Analysis of PDEs 2020-02-28 v1

Abstract

In this paper we prove the validity of Gibbons' conjecture for the quasilinear elliptic equation Δpu=f(u) -\Delta_p u = f(u) on RN.\mathbb{R}^N. The result holds true for (2N+2)/(N+2)<p<2(2N+2)/(N+2) < p < 2 and for a very general class of nonlinearity ff.

Keywords

Cite

@article{arxiv.2002.11970,
  title  = {On the Gibbons' conjecture for equations involving the $p$-Laplacian},
  author = {Francesco Esposito and Alberto Farina and Luigi Montoro and Berardino Sciunzi},
  journal= {arXiv preprint arXiv:2002.11970},
  year   = {2020}
}