Topology of singular set of semiconcave function via Arnaud's theorem

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2022-10-27 DOI:10.3934/cpaa.2023053

Tianqi Shi, Wei Cheng, Jiahui Hong

引用次数: 0

Abstract

We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The proof is based on a theorem by Marie-Claude Arnaud (M.-C. Arnaud, \textit{Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation}. Nonlinearity, \textbf{24}(1): 71-78, 2011.). We also gave a new proof of the theorem in time-dependent case.

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基于Arnaud定理的半凹函数奇异集拓扑

我们一般证明了具有线性模的半凹函数奇异集的某个子集的（局部）路径连通性。从某种意义上说，这个结果是最优的。该证明基于Marie-Claude Arnaud的一个定理（M.-C.Arnaud，\textit{伪图和Lax-Oleinik半群：几何和动力学解释}。非线性，\textbf｛24｝（1）：71-781011。）。我们还给出了该定理在时间依赖情况下的新证明。

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

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.

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