On the Maxwell and Friedrichs/Poincare Constants in ND

2017/03/17 by Dirk Pauly, Pauly, Dirk · 1 citation
Computer Science · Mathematics · #35A23 #35E10 #35F15 #35Q61 #35R45 #46E40 #53A45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1703.05966

openalex publication_date 2017/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for bounded and convex domains in arbitrary dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincare's constants, respectively. Especially, the second positive Maxwell eigenvalues in ND are bounded from below by the square root of the second Neumann-Laplace eigenvalue.

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