The Minkowski inequalities for ( p , α ) $(p,\alpha)$ -torsional rigidity and the extensions on Orlicz spaces

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-08-18 DOI:10.1002/mana.70032

Zhen-Hui Bu, Meng Qin, Denghui Wu

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引用次数: 0

Abstract

In this paper, we prove the functional Minkowski inequality for $(p, α)$ -torsional rigidity under suitable regularity assumptions, where $(p, α)$ -torsional rigidity can be formulated as the weak solution of an elliptic boundary value problem of the $p$ -Laplacian. We also establish the Orlicz Brunn–Minkowski and Orlicz Minkowski inequalities for $(p, α)$ -torsional rigidity, which are extensions of the Brunn–Minkowski and Minkowski inequalities for torsional rigidity. Finally, we describe the equivalence between the Orlicz Brunn–Minkowski inequality and the Orlicz Minkowski inequality.

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（p, α）$ (p,\ α)$ -扭转刚度的Minkowski不等式及其在Orlicz空间上的扩展

在适当的正则性假设下，证明了（p, α）$ (p,\ α)$ -扭转刚度的泛函Minkowski不等式，其中(p，α)$ (p,\ α)$ -扭转刚度可以表示为p$ p$ -拉普拉斯算子椭圆边值问题的弱解。我们还建立了（p, α）$ (p,\ α)$ -扭转刚度的Orlicz Brunn-Minkowski和Orlicz Minkowski不等式，它们是扭转刚度的Brunn-Minkowski和Minkowski不等式的推广。最后，我们描述了Orlicz Brunn-Minkowski不等式与Orlicz Minkowski不等式之间的等价性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index