Connections between optimal constants in some norm inequalities for differential forms
Analysis of PDEs
2020-04-10 v2
Abstract
We derive an improved Poincar\'e inequality in connection with the Babu\v{s}ka-Aziz and Friedrichs-Velte inequalities for differential forms by estimating the domain specific optimal constants figuring 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.
Cite
@article{arxiv.1808.06420,
title = {Connections between optimal constants in some norm inequalities for differential forms},
author = {Sándor Zsuppán},
journal= {arXiv preprint arXiv:1808.06420},
year = {2020}
}
Comments
14 pages, 0 figures