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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 2, 2020, pp. 171–184
DOI: 10.4171/ZAA/1656

Published online: 2020-04-07

Connections Between Optimal Constants in some Norm Inequalities for Differential Forms

Sándor Zsuppán[1]

(1) Berzsenyi Dániel Evangélikus Gimnázium, Sopron, Hungary

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.

Keywords: Babuška–Aziz inequality, Friedrichs–Velte inequality, improved Poincaré inequality, optimal constants

Zsuppán Sándor: Connections Between Optimal Constants in some Norm Inequalities for Differential Forms. Z. Anal. Anwend. 39 (2020), 171-184. doi: 10.4171/ZAA/1656