Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

2013/02/07 by Barbara Brandolini, Brandolini, B., Ferdınando Chıacchıo +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1302.1795

openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue μ₁(Ω) for the p-Laplace operator in a Lipschitz, bounded domain Ω in \Rⁿ. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω.

Citations

• An optimal Poincaré inequality for convex domains

Cited by

• First Eigenvalue and Torsional Rigidity: Isoperimetric Inequalities for the Fractional Laplacian

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