非线性次椭圆方程障碍问题很弱解的高阶可积性  

Higher Integrability for Very Weak Solutions of Obstacle Problems to Nonlinear Subelliptic Equations

作　　者：杜广伟[1] 钮鹏程[1] 

机构地区：[1]西北工业大学应用数学系,西安710129

出　　处：《数学物理学报（A辑）》2017年第1期122-145,共24页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271299)~~

摘　　要：该文首先证明了一类由满足Hrmander条件的向量场构成的次椭圆方程K_(φ,u_0)~T-障碍问题很弱解的局部高阶可积性,进而说明了其很弱解即为经典意义下的弱解.作为其应用,得到了障碍问题很弱解的紧性结果.此外,在当区域Ω满足某容度条件假设时,证明了上述障碍问题很弱解的全局高阶可积性.In this paper we first establish the local higher integrability for very weak solutions of the K^rφ,u0-obstacle problems to the nonlinear subelliptic equations constructed by Hormander vector fields which implies the very weak solutions are classical weak solutions. As an application, the compactness results are obtained. We also derive the global higher integrability for very weak solutions of the K^rφ,u0-obstacle problems with a capacitary condition on Ω.

关 键 词：非线性次椭圆方程 障碍问题 很弱解 高阶可积性 紧性 

分 类 号：O175.2[理学—数学]