\海森堡群中具有漂移的亚椭圆系统的(C^{1}\)正则性:超二次可控增长

IF 1.7 4区 数学 Q1 Mathematics
Guoqiang Duan, Jialin Wang, Dongni Liao
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引用次数: 0

摘要

我们研究了海森堡群中超二次可控结构条件下发散形式的非线性亚椭圆系统的内部正则性。基于$\mathcal{A}$谐波逼近技术的广义化,建立了带漂移项的亚椭圆系统的矢量值解的水平梯度的$C^{1}$正则性。特别是,我们的结果是最优的,因为在赫尔德连续系数的情况下,我们直接获得了正则集合上弱解水平梯度的最优赫尔德指数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
\(C^{1}\)-Regularity for subelliptic systems with drift in the Heisenberg group: the superquadratic controllable growth
We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis of a generalization of the $\mathcal{A}$ -harmonic approximation technique, $C^{1}$ -regularity is established for horizontal gradients of vector-valued solutions to the subelliptic systems with drift term. Specially, our result is optimal in the sense that in the case of Hölder continuous coefficients we directly attain the optimal Hölder exponent for the horizontal gradients of weak solutions on the regular set.
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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