具有加权有界失真映射的Schwarz引理的一个版本

IF 0.4 Q4 MATHEMATICS

Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya Pub Date : 2021-04-18 DOI:10.33048/semi.2021.18.029

M. V. Tryamkin

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引用次数: 0

摘要

我们考虑一类映射，它推广了qusiregular映射。该类的每一个映射都定义在欧氏n空间的一个域中，并具有以下性质：它是开的、连续的和离散的，它局部属于Sobolev类W1q，它具有有限失真和非负Jacobian，它的加权（p，q）-失真函数可积到一定的幂，取决于p和q，其中n−1n。所使用的技术是基于球面对称化过程和Gr-otzsch聚敛器的概念。

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A version of Schwarz's lemma for mappings with weighted bounded distortion

We consider the class of mappings generalizing qusiregular mappings. Every mapping from this class is de ned in a domain of Euclidean n-space and possesses the following properties: it is open, continuous, and discrete, it belongs locally to the Sobolev classW 1 q , it has nite distortion and nonnegative Jacobian, and its function of weighted (p, q)-distortion is integrable to a certian power depending on p and q, where n − 1 < q 6 p < ∞. We obtain an analog of Schwarz's lemma for such mappings provided that p > n. The technique used is based on the spherical symmetrization procedure and the notion of Gr otzsch condenser.

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来源期刊

Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya MATHEMATICS-

CiteScore

1.00

自引率

25.00%

发文量