Quasiconformal, Lipschitz, and BV mappings in metric spaces

IF 1.3 3区数学 Q1 MATHEMATICS Advances in Calculus of Variations 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}

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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

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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