Heisenberg群上高阶退化椭圆方程解的Morrey正则性  

Morrey regularity of higher order degenerate elliptic equation on the Heisenberg group

作　　者：李俊兵[1] 魏娜[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》2009年第4期459-462,共4页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基础研究计划资助项目(2006A09);西北工业大学科技创新基金(2007KJ01012))

摘　　要：为了得到Heisenberg群上具有不连续系数的高阶退化椭圆方程强解的Morrey正则性,利用了Heisenberg群上奇异积分和奇异积分与BMO函数的交换子在Morrey空间上的有界性,通过凝固系数法,并将高阶向量场导数表示为奇异积分及交换子的和,由加权Morrey半范数的内插不等式得到高阶退化椭圆方程强解在Morrey空间中的正则性.The Morrey berg group is obtained with the BMO function regularity of higher order degenerate elliptic equation with VMO coefficient on the Heisenby using the boundedness of singular integrals and the commutators of singular integrals on the Morrey space. Furthermore, higher order derivative of vector field by the sum of singular integrals and the commutators of singular integrals, and the Morrey regulari is represented ty of strong solution to higher order degenerate elliptic equation is achieved through freezing coefficient.

关 键 词：HEISENBERG群 MORREY空间 奇异积分 VMO(零平均震荡) BMO(有界平均震荡) 

分 类 号：O175.24[理学—数学]