p-扭转刚性问题的形状优化

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1625-1633.

p-扭转刚性问题的形状优化

阮其华()

^{莆田学院数学与金融学院福建莆田 351100}

收稿日期:2020-05-07 出版日期:2021-12-26 发布日期:2021-12-02
作者简介:阮其华, E-mail: ruanqihua@163.com
基金资助:
国家自然科学基金(11971253);福建省自然科学基金(2017J01563);金融数学福建省高校重点实验室

Shape Optimization for p-Torsional Rigidity Problems

Qihua Ruan()

^{School of Mathematics and Finance, Putian University, Fujian Putian 351100}

Received:2020-05-07 Online:2021-12-26 Published:2021-12-02
Supported by:
the NSFC(11971253);the NSF of Fujian Province(2017J01563);the Key Laboratory of Financial Mathematics of Fujian Province University

摘要/Abstract

摘要：

该文对p-扭转刚性问题构造了一个域泛函，证明该域泛函的最优形状是球形.利用域导数的方法，给出p-扭转刚性超定问题的另一种证明.

关键词: 最优区域, 超定问题, p-扭转刚性

Abstract:

In this paper, we construct a shape functional for p-torsional rigidity problems and prove that the optimal shape of this shape functional is a ball. Using a method of the shape derivative, we give an alternative proof of the overdetermined problem for p-torsional rigidity.

Key words: Shape optimiztion, Overdetermined problem, p-Torsional rigidity

中图分类号:

O175.2

阮其华. p-扭转刚性问题的形状优化[J]. 数学物理学报, 2021, 41(6): 1625-1633.

Qihua Ruan. Shape Optimization for p-Torsional Rigidity Problems[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1625-1633.

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