Upper bound for the first non-zero eigenvalue of the p-Laplacian

2018/05/28 by Sheela Verma, Verma, Sheela
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1805.11040

openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed hypersurface in ℝⁿ and Ω be a bounded domain such that M= ∂Ω. In this article, we obtain an upper bound for the first non-zero eigenvalue of the following problems. \beginitemize \item Closed eigenvalue problem: % Δ_p u = λ_p |u|^p-2 u on M. \item Steklov eigenvalue problem: Δ_pu · amp;= · amp; 0 · amp; in Ω,
|∇ u|^p-2 (∂ u)/(∂ ν) · amp;= · amp; μ_p |u|^p-2 u · amp; on M . \enditemize

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