具有控制拉普拉斯和Hölder连续性的拟共形映射

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2019-06-01 DOI:10.5186/AASFM.2019.4440

D. Kalaj, Arsen Zlaticanin

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引用次数: 5

摘要

摘要我们证明了单位球B∧R, n≥2在C-Jordan域Ω上的每一个k -拟共形映射w是Hölder连续的，且常数α = 2 - n p，只要它的弱拉普拉斯函数∆w在L(B)中，对于某些n/2 < p < n。特别是对于∆w∈L(B)，对于每一个0 < α < 1，它是Hölder连续的。最后，对于p > n，我们证明了w是Lipschitz连续的，这个结果的证明已经由第一作者和Saksman在[16]中勾画出来。本文包含[17]中公布的一些结果的证明。

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Quasiconformal mappings with controlled Laplacian and Hölder continuity

Abstract. We prove that every K-quasiconformal mapping w of the unit ball B ⊂ R, n ≥ 2 onto a C-Jordan domain Ω is Hölder continuous with constant α = 2 − n p , provided its weak Laplacian ∆w is in L(B) for some n/2 < p < n. In particular it is Hölder continuous for every 0 < α < 1 provided that ∆w ∈ L(B). Finally for p > n, we prove that w is Lipschitz continuous, a result, whose proof has been already sketched in [16] by the first author and Saksman. The paper contains the proofs of some results announced in [17].

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.