# “On the first nontrivial Neumann eigenvalue of the infinity Laplacian” – Carlo Nitsch (Università Federico II, Napoli)

#### Venue

Sala Seminari (Dip. Matematica).

#### Abstract

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.

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