The Neumann eigenvalue problem for the -Laplacian

  • L. Esposito

    Università di Salerno, Fisciano (Sa), Italy
  • Bernd Kawohl

    Universität Köln, Germany
  • Carlo Nitsch

    Università degli Studi di Napoli Federico II, Italy
  • Cristina Trombetti

    Università degli Studi di Napoli Federico II, Italy

Abstract

The first nontrivial eigenfunction of the Neumann eigenvalue problem for the -Laplacian, suitably normalized, converges to a viscosity solution of an eigenvalue problem for the -Laplacian as . We show among other things that the limiting eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.

Cite this article

L. Esposito, Bernd Kawohl, Carlo Nitsch, Cristina Trombetti, The Neumann eigenvalue problem for the -Laplacian. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 2, pp. 119–134

DOI 10.4171/RLM/697