由Baouendi-Grushin向量场构成的退化椭圆方程组弱解梯度的L^p估计  

L^p estimates for gradients of weak solutions to degenerate elliptic systems constituted by Baouendi-Grushin vector fields

作　　者：董艳[1] 钮鹏程[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710129

出　　处：《纺织高校基础科学学报》2011年第3期373-376,381,共5页Basic Sciences Journal of Textile Universities

摘　　要：研究了一类与Baouendi-Grushin向量场族相关的具有不连续系数的退化椭圆方程组.通过建立Caccioppoli型不等式并利用反向Hlder不等式,得到了该类方程组弱解梯度的局部Lp估计,从而提升了弱解的光滑性.A class of degenerate elliptic systems related to Baouendi-Grushin vector fields are studied when the coefficients are discontinuous.By establishing a Caccioppoli inequality and using the reverse Hlder inequality,the Lp estimates for the gradients of weak solutions to the system are obtained and the regularity of the weak solution is lifted.

关 键 词：退化椭圆方程组 Baouendi-Grushin向量场 VMO函数 Lp估计 

分 类 号：O174.54[理学—数学]