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中国科学院大学学报 ›› 2014, Vol. 31 ›› Issue (1): 10-16.DOI: 10.7523/j.issn.2095-6134.2014.01.003

• 数学与物理学 • 上一篇    下一篇

Carnot群上散度型退化椭圆方程组的内Morrey估计

朱茂春, 冯晓晶   

  1. 西北工业大学应用数学系, 西安 710129
  • 收稿日期:2012-12-05 修回日期:2013-03-29 发布日期:2014-01-15
  • 通讯作者: 朱茂春,E-mail:zhumaochun2006@126.com;冯晓晶,E-mail:fxj467@126.com
  • 基金资助:

    Supported by National Natural Science Foundation of China(11271299, 11001221) and Northewstern Polytechnical University jichu yanjiu jijin tansuo xiangmu(JC201124)

Interior Morrey estimates for divergence degenerate elliptic systems in Carnot groups

ZHU Maochun, FENG Xiaojing   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
  • Received:2012-12-05 Revised:2013-03-29 Published:2014-01-15
  • Supported by:

    Supported by National Natural Science Foundation of China(11271299, 11001221) and Northewstern Polytechnical University jichu yanjiu jijin tansuo xiangmu(JC201124)

摘要:

X1,…,Xq是Carnot群G =(R no)(q<n)上的一组水平向量场的基. 主要考虑下面的散度型退化方程组
10???
其中,系数aαβij是Ω⊂;G上的实的有界VMOloc(Ω)函数并且满足强 Legendre条件. 得到该方程组弱解的内Morrey估计.

关键词: Carnot 群, 次椭圆方程组, Morrey估计

Abstract:

Let X1,…,Xq be the basis of the space of horizontal vector fields on a homogeneous Carnot group G =(R n,o) (q<n). The interior Morrey estimates for weak solutions to the following divergence degenerate elliptic system
10???
are obtained when the coefficients aαβij satisfy the strong Legendre condition in Ω⊂ G and belong to the space VMOloc(Ω).

Key words: Carnot group, subelliptic systems, Morrey estimates

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