Quasiconformal, Lipschitz, and BV mappings in metric spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-12 DOI:10.1515/acv-2022-0071

Panu Lahti

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引用次数: 0

Abstract

Consider a mapping f : X → Y

{f\colon X\to Y}

between two metric measure spaces. We study generalized versions of the local Lipschitz number Lip ⁡ f

{\operatorname{Lip}f}

, as well as of the distortion number H f

{H_{f}}

that is used to define quasiconformal mappings. Using these numbers, we give sufficient conditions for f being a BV mapping f ∈ BV loc ⁢ ( X ; Y )

{f\in\mathrm{BV}_{\mathrm{loc}}(X;Y)}

or a Newton–Sobolev mapping f ∈ N loc 1 , p ⁢ ( X ; Y )

{f\in N_{\mathrm{loc}}^{1,p}(X;Y)}

, with 1 ≤ p < ∞

{1\leq p<\infty}

查看原文本刊更多论文

度量空间中的准共形、Lipschitz 和 BV 映射

考虑两个度量空间之间的映射 f : X → Y {f\colon X\to Y} 。我们研究局部 Lipschitz 数 Lip f {\operatorname{Lip}f} 的广义版本，以及用于定义准共形映射的变形数 H f {H_{f}} 的广义版本。利用这些数字，我们给出了 f 是 BV 映射 f∈ BV loc ( X ; Y ) {f\in\mathrm{BV}_{\mathrm{loc}}(X. Y)} 或牛顿映射 f∈ BV loc ( X ; Y ) {f\in\mathrm{BV}_{\mathrm{loc}}(X. Y)} 的充分条件；Y)} 或者牛顿-索博列夫映射 f∈ N loc 1 , p ( X ; Y ) {f\in N_{\mathrm{loc}}^{1,p}(X;Y)} , 其中 1 ≤ p < ∞ {1\leq p<\infty} 。

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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.