On the Maxwell and Friedrichs/Poincare Constants in ND
arXiv:1703.0596618 citationsh-index: 22
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Provides theoretical bounds for Maxwell constants in convex domains, which is a foundational result for numerical analysis and PDE theory.
The paper proves that for bounded convex domains in any dimension, Maxwell constants are bounded by Friedrichs' and Poincaré constants, and lower bounds the second Maxwell eigenvalue by the square root of the second Neumann-Laplace eigenvalue.
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.