A Note about Torsional Rigidity and Euclidean Moment of Inertia of Plane Domains
- 作者: Salakhudinov R.1
-
隶属关系:
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- 期: 卷 39, 编号 6 (2018)
- 页面: 826-834
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202479
- DOI: https://doi.org/10.1134/S1995080218060161
- ID: 202479
如何引用文章
详细
Denote by P(G) the torsional rigidity of a simply connected plane domain G, and by I2(G) the Euclidean moment of inertia of G. In 1995 F.G. Avkhadiev proved that P(G) and I2(G) are comparable quantities in sense of Pólya and Szegö. Moreover, it was shown that the ratio P(G) /I2(G) belongs to the segment [1, 64]. We investigate the following conjecture P(G) ≥ 3I2(G), where G is a simply connected domain. We prove that the conjecture is true for polygonal domains circumscribed about a circle. For convex domains we show sharp isoperimetric inequalities, which justify the conjecture, in particular, we prove that P(G) > 2I2(G). Some aspects of approximate formulas for P(G) are also discussed.
作者简介
R. Salakhudinov
N. I. Lobachevskii Institute of Mathematics and Mechanics
编辑信件的主要联系方式.
Email: rsalakhud@gmail.com
俄罗斯联邦, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008