The optimal problems for torsional rigidity

Jin Yang; Zhenzhen Wei; Jin Yang; Zhenzhen Wei

doi:10.3934/math.2021271

AIMS Mathematics

2021, Volume 6, Issue 5: 4597-4613. doi: 10.3934/math.2021271

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Research article

The optimal problems for torsional rigidity

Jin Yang ,
Zhenzhen Wei ^,

Department of Mathematics, Hubei Minzu University, Enshi, Hubei, China 445000

Received: 28 September 2020 Accepted: 25 January 2021 Published: 22 February 2021
MSC : 53A15, 52A39

In this paper, we consider the optimization problems associated with the nonhomogeneous and homogeneous Orlicz mixed torsional rigidities by investigating the properties of the corresponding mixed torsional rigidity. As the main results, the existence and the continuity of the solutions to these problems are proved.
- geominimal surface area,
- Petty bodies,
- torsional rigidity,
- torsional measure,
- mixed torsional rigidity
Citation: Jin Yang, Zhenzhen Wei. The optimal problems for torsional rigidity[J]. AIMS Mathematics, 2021, 6(5): 4597-4613. doi: 10.3934/math.2021271

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Abstract

In this paper, we consider the optimization problems associated with the nonhomogeneous and homogeneous Orlicz mixed torsional rigidities by investigating the properties of the corresponding mixed torsional rigidity. As the main results, the existence and the continuity of the solutions to these problems are proved.

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