在满足均匀球条件的域中存在螺旋度最大化问题的最优域

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-14 DOI:10.1063/5.0163183

Wadim Gerner

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引用次数: 0

摘要

在本研究中，我们提出了一个通用框架，只要所求目标函数满足某些属性，它就能保证在满足均匀球条件的 C1,1-regular 域类中，等周问题存在最优域。然后，我们验证了 [Cantarella 等人，J. Math. Phys. 41, 5615 (2000)]中研究的螺旋度等周问题满足我们框架的条件，并因此确定了给定域类中最优域的存在性。此外，我们还用同样的框架证明了第一卷曲特征值问题的均匀 C1,1 域中最优域的存在性，该问题最近在 [Enciso 等人，Trans. Am. Math. Soc. 377, 4519-4540 (2024)] 中对其他类别的域进行了研究。

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Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition

In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of C1,1-regular domains satisfying a uniform ball condition as long as the desired objective function satisfies certain properties. We then verify that the helicity isoperimetric problem studied in [Cantarella et al., J. Math. Phys. 41, 5615 (2000)] satisfies the conditions of our framework and hence establish the existence of optimal domains within the given class of domains. We additionally use the same framework to prove the existence of optimal domains among uniform C1,1-domains for a first curl eigenvalue problem which has been studied recently for other classes of domains in [Enciso et al., Trans. Am. Math. Soc. 377, 4519–4540 (2024)].

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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