# On the Maxwell and Friedrichs/Poincare Constants in ND

## TL;DR

This paper establishes bounds for Maxwell constants in convex domains across any dimension, linking them to Friedrichs' and Poincare's constants, and relates Maxwell eigenvalues to Laplace eigenvalues.

## Contribution

It proves that Maxwell constants are bounded by Friedrichs' and Poincare's constants in convex domains of arbitrary dimensions, providing new bounds for Maxwell eigenvalues.

## Key findings

- Maxwell constants are bounded by Friedrichs' and Poincare's constants.
- Second Maxwell eigenvalues are bounded below by the square root of the second Neumann-Laplace eigenvalue.
- Results hold for bounded convex domains in any dimension.

## 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.