The Neumann eigenvalue problem for the $\\infty$-Laplacian

The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian converges, as $p$ goes to $\\infty$, to a viscosity solution of a suitable eigenvalue problem for the $\\infty$-Laplacian. We show among other things that the limiting eigenvalue is in fact
the first nonzero eigenvalue, and derive a number consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian. This is a joint work with L.Esposito, B.Kawohl and C.Trombetti.