The ∞-Laplacian first eigenvalue problem

Abstract

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In Section 5 we make some remarks on the simplicity of the first eigenvalue of Δ∞: this will be the object of a joint work with A. Wagner (see [BW]).