有限偏差函数与调和函数  

Mappings of finite distortion and harmonic functions

作　　者：冯小高[1] 

机构地区：[1]西华师范大学数学与信息学院,四川南充637002

出　　处：《纯粹数学与应用数学》2016年第2期119-126,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(10871211);西华师范大学青年教师资助项目(13D017);西华师范大学科研基金(08B032)

摘　　要：分别借助解析函数与调和函数两类函数的Dirichlet积分,利用相关文献给定边界值的拟共形映射极值伸缩商的估计方法,通过有限偏差函数和拟共形映射的关系估计了具有给定边界值的有限偏差函数的极值伸缩商.得到了解析函数的Dirichlet积分在有限偏差函数下具有拟不变性,同时给出有限偏差函数极值伸缩商的下界估计.On the basis of Dirichlet integral of holomorphic functions and harmonic functions,rspectively, We shall estimate the extremal maximal dilatation of mappings of finite ditortion with given boundary values by the methods of estimating the extremal maximal dilatation of quasiconformal mappings given boundary values and by using the relation between mappings of finite distortion and quasiconformal mappings. we obtain the quasi-invariance property of the Dirichlet integral under mappings of finite distortion and give the concrete estimates on the extremal dilatation from below.

关 键 词：有限偏差函数 调和函数 DIRICHLET积分 极值伸缩商 拟共形映射 

分 类 号：O174[理学—数学]