Le, An2021-07-202021-07-202006-09-18Lê, A. (2006). On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian. <i>Electronic Journal of Differential Equations, 2006</i>(111), pp. 1-9.1072-6691https://hdl.handle.net/10877/13984Let Λp p be the best Sobolev embedding constant of W1,p(Ω) ↪ Lp(∂Ω), where Ω is a smooth bounded domain in ℝN. We prove that as p → ∞ the sequence Λp converges to a constant independent of the shape and the volume of Ω, namely 1. Moreover, for any sequence of eigenfunctions up (associated with Λp), normalized by ∥up∥L∞(∂Ω) = 1, there is a subsequence converging to a limit function u∞ which satisfies, in the viscosity sense, an ∞-Laplacian equation with a boundary condition.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear elliptic equationsEigenvalue problemsp-LaplacianNonlinear boundary conditionSteklov problemViscosity solutionsArticle