(K1,K2)-拟正则映射的Hölder连续性和几乎处处可微性

高红亚, 刘超, 李军伟

数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 721-726.

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数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 721-726. DOI: 10.12386/A2012sxxb0069
论文

(K1,K2)-拟正则映射的Hölder连续性和几乎处处可微性

    高红亚1, 刘超1, 李军伟2
作者信息 +

Hölder Continuity and Differentiability Almost Everywhere of (K1,K2)-Quasiregular Mappings

    Hong Ya GAO1, Chao LIU1, Jun Wei LI2
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摘要

考虑(K1,K2)-拟正则映射. 利用Morrey引理和等周不等式,证明了在其定义域中的任意紧子集上,每个(K1,K2)-拟正则映射都满足具有指数α的Hölder条件,这里  本文也得到了(K1,K2)-拟正则映射的几乎处处可微性.

Abstract

We deal with (K1,K2)-quasiregular mappings. It is shown, by Morrey’s Lemma and isoperimetric inequality, that every (K1,K2)-quasiregular mapping satisfies a Hölder condition with exponent α on compact subsets of its domain, where  Differentiability almost everywhere of (K1,K2)-quasiregular mappings is also derived. Keywords (K1,K2)-quasiregular mapping; Hölder continuity; differentiability almost everywhere; Morrey’s lemma

关键词

(K1,K2)-拟正则映射 / Hö / lder连续性 / 几乎处处可微性 / O21Morrey引理

Key words

(K1,K2)-quasiregular mapping / Hö / lder continuity / differentiability almost everywhere / Morrey’s lemma

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高红亚, 刘超, 李军伟. (K1,K2)-拟正则映射的Hölder连续性和几乎处处可微性. 数学学报, 2012, 55(4): 721-726 https://doi.org/10.12386/A2012sxxb0069
Hong Ya GAO, Chao LIU, Jun Wei LI. Hölder Continuity and Differentiability Almost Everywhere of (K1,K2)-Quasiregular Mappings. Acta Mathematica Sinica, Chinese Series, 2012, 55(4): 721-726 https://doi.org/10.12386/A2012sxxb0069

参考文献

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基金

国家自然科学基金资助项目(10971224);河北省自然科学基金资助项目(A2011201011)

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