Minimizing movements for anisotropic and inhomogeneous mean curvature flows

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-04 DOI:10.1515/acv-2022-0102

Antonin Chambolle, Daniele de Gennaro, Massimiliano Morini

引用次数: 1

Abstract

Abstract In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions à la Luckhaus–Sturzenhecker to such flows, the latter result holding in low dimension and conditionally to the convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows one to simplify many arguments.

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各向异性和非均匀平均曲率流的最小运动

摘要本文讨论了具有强迫和迁移性的各向异性和非均匀平均曲率流，并证明了最小化运动格式收敛于这类流的水平集/黏性解和分布解，后者的结果在低维条件下保持能量收敛。通过这样做，我们通过消除平移不变性假设来推广最近关于平均曲率演化的工作，这在经典理论中允许简化许多论点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.