407 research outputs found
On Maxwell's and Poincare's Constants
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.Comment: Key Words: Maxwell's equations, Maxwell constant, second Maxwell
eigenvalue, electro statics, magneto statics, Poincare's inequality,
Friedrichs' inequality, Poincare's constant, Friedrichs' constan
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