On the Maxwell Inequalities for Bounded and Convex Domains

TL;DR

This paper establishes bounds for Maxwell constants in bounded convex domains, relating them to Friedrichs' and Poincare's constants, thereby enhancing understanding of electromagnetic inequalities in such geometries.

Contribution

It provides new bounds for Maxwell constants in convex domains, connecting them with classical Friedrichs' and Poincare's inequalities, which was previously unexplored.

Findings

Maxwell constants are bounded by Friedrichs' and Poincare's constants.

The bounds are valid specifically for bounded convex domains in three dimensions.

This work improves theoretical understanding of electromagnetic inequalities in convex geometries.

Abstract

For a bounded and convex domain in three dimensions we show that the Maxwell constants are bounded from below and above by Friedrichs' and Poincare's constants.