变分卡纳姆-赫尔弗里希流的广义最小化运动

IF 1.3 3区数学 Q1 MATHEMATICS Advances in Calculus of Variations Pub Date : 2024-01-12 DOI:10.1515/acv-2022-0056

Katharina Brazda, Martin Kružík, Ulisse Stefanelli

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引用次数: 0

摘要

Canham-Helfrich 函数的梯度流是通过广义最小化运动方法解决的。我们证明了变曲率的瓦瑟斯坦空间中解的存在性，以及直径的上下限。在多面覆盖的 C 1 , 1 {C^{1,1}} 曲面这一更为常规的环境中，我们提供了 Canham-Helfrich 能量的 Li-Yau 型估计，并证明了沿演化过程的多重性守恒。

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Generalized minimizing movements for the varifold Canham–Helfrich flow

The gradient flow of the Canham–Helfrich functional is tackled via the generalized minimizing movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered C 1 , 1

{C^{1,1}}

surfaces, we provide a Li–Yau-type estimate for the Canham–Helfrich energy and prove the conservation of multiplicity along the evolution.

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来源期刊

Advances in Calculus of Variations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.

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