The Neumann eigenvalue problem for the -Laplacian
L. Esposito
Università di Salerno, Fisciano (Sa), ItalyBernd Kawohl
Universität Köln, GermanyCarlo Nitsch
Università degli Studi di Napoli Federico II, ItalyCristina 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