On Maxwell's and Poincare's Constants
Analysis of PDEs
2014-03-12 v4 Numerical Analysis
Abstract
We prove that for bounded and convex domains in three dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincar\'e's constants. In other words, the second Maxwell eigenvalues lie between the square roots of the second Neumann-Laplace and the first Dirichlet-Laplace eigenvalue.
Keywords
Cite
@article{arxiv.1311.2186,
title = {On Maxwell's and Poincare's Constants},
author = {Dirk Pauly},
journal= {arXiv preprint arXiv:1311.2186},
year = {2014}
}
Comments
Key Words: Maxwell's equations, Maxwell constant, second Maxwell eigenvalue, electro statics, magneto statics, Poincare's inequality, Friedrichs' inequality, Poincare's constant, Friedrichs' constant