契格常数的圆柱形估计及其应用

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI:10.1016/j.matpur.2024.103633

Aldo Pratelli , Giorgio Saracco

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引用次数: 0

摘要

证明了柱体Ω×（0，L）的Cheeger常数的下界，其中Ω是开有界集。因此，我们得到了形状泛函的最小值的存在性，该泛函定义为p-拉普拉斯的第一个Dirichlet特征值与Cheeger常数的p次幂之间的比率，在任何RN的有界凸集内。这正面地解决了Parini （J. Convex Anal）提出的开放性猜想。（2017）)和Briani-Buttazzo-Prinari (Ann。Mat. Pura apple。(2023))。

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Cylindrical estimates for the Cheeger constant and applications

We prove a lower bound for the Cheeger constant of a cylinder

Ω \times (0, L)

, where Ω is an open and bounded set. As a consequence, we obtain existence of minimizers for the shape functional defined as the ratio between the first Dirichlet eigenvalue of the p-Laplacian and the p-th power of the Cheeger constant, within the class of bounded convex sets in any

R^{N}

. This positively solves open conjectures raised by Parini (J. Convex Anal. (2017)) and by Briani–Buttazzo–Prinari (Ann. Mat. Pura Appl. (2023)).

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来源期刊

Journal de Mathematiques Pures et Appliquees 数学-数学

CiteScore

4.30

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.