一类非迷向Heisenberg群上凸函数的比较原理  

Comparison Principle for Convex Functions in a Class of Anisotropic Heisenberg Group

作　　者：李虎俊[1] 王彦林[2] 徐飞[3] 李闻白[4] 

机构地区：[1]湖北职业技术学院,孝感432000 [2]西安工程大学理学院,西安710048 [3]西安工业大学计算机科学与工程学院,西安710032 [4]西北工业大学航海学院,西安710072

出　　处：《西安工业大学学报》2010年第5期499-505,共7页Journal of Xi’an Technological University

摘　　要：Homander向量场上弱凸函数的单调性质对研究完全非线性次椭圆方程的正则性起关键作用.针对一类特殊的Homander向量场——非迷向Heisenberg群H2(a,b),通过构造辅助函数,利用基于群结构的散度定理建立了H2(a,b)上弱H-凸函数的比较原理,得到了与之相应的非线性次椭圆算子的单调性质.研究结果有望为进一步讨论高维Heisenberg群上弱凸函数的性质和高阶非线性次椭圆方程的正则性提供理论基础.The monotonicity of weak convex functions on Homander vector fields plays an important role in studying the regularity of fully nonlinear subelliptic equations.For a special class of the Homander vector fields——anisotropic Heisenberg group H2（a,b）,a comparison principle for the weak H-convex functions and the corresponding monotonicity of the nonlinear subelliptic operator on H2（a,b） are obtained by constructing auxiliary functions and using the divergence theorem based on the group structure.The results are expected to provide some theoretical basis for further studying the properties of weak convex functions on higher-dimension Heisenberg groups and the regularity of higher-order nonlinear subelliptic equations.

关 键 词：非迷向Heisenberg群 凸函数 比较原理 散度定理 

分 类 号：O175.2[理学—数学]