On Maxwell's and Poincaré's constants
Dirk Pauly · Discrete and Continuous Dynamical Systems - S · 2014
We prove that for bounded and convex domains in three dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincaré'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.