Connections Between Optimal Constants in some Norm Inequalities for Differential Forms

摘要

We derive an improved Poincare inequality in connection with the Babuska-Aziz and Friedrichs-Velte inequalities for differential forms by estimating the domain specific 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.