Connections Between Optimal Constants in some Norm Inequalities for Differential Forms

Abstract

We derive an improved Poincaré inequality in connection with the Babuška–Aziz and Friedrichs–Velte inequalities for differential forms by estimating the domain specific optimal constants in the respective inequalities with each other provided the domain supports the Hardy inequality. We also derive upper estimates for the constants of a star-shaped domain by generalizing the known Horgan–Payne type estimates for planar and spatial domains to higher dimensional ones.