微分形式范数不等式中最优常数之间的联系

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2018-08-20 DOI:10.4171/ZAA/1656

S'andor Zsupp'an

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引用次数: 0

摘要

在给定的域支持Hardy不等式的情况下，我们通过估计域内特定的最优常数，推导出一个改进的庞加莱不等式与Babuska-Aziz不等式和Friedrichs-Velte不等式的微分形式。我们还通过将已知的平面和空间域的Horgan-Payne型估计推广到高维域，推导出星形域常数的上估计。

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Connections Between Optimal Constants in some Norm Inequalities for Differential Forms

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 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.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.