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
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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。
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来源期刊
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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