On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian
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Date
2006-09-18
Authors
Le, An
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
Let 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.
Description
Keywords
Nonlinear elliptic equations, Eigenvalue problems, p-Laplacian, Nonlinear boundary condition, Steklov problem, Viscosity solutions
Citation
Lê, A. (2006). On the first eigenvalue of the Steklov eigenvalue problem for the infinity Laplacian. Electronic Journal of Differential Equations, 2006(111), pp. 1-9.
Rights
Attribution 4.0 International