Steklov eigenvalues for the ∞-Laplacian

Abstract. We study the Steklov eigenvalue problem for the ∞-laplacian. To this end we consider the limit as p→ ∞ of solutions of −∆pup = 0 in a domain Ω with |∇up|p−2∂up/∂ν = λ|u|p−2u on ∂Ω. We obtain a limit problem that is satisfied in the viscosity sense and a geometric characterization of the second eigenvalue. 1. Introduction. Let ∆pu = div (|∇u|p−2∇u) be the p−laplacian. The limit operato