矩形上组合偏差函数的极值问题  

Extremal Problem of Combined Distortion on Rectangle

作　　者：唐茹月 刘初玥 冯小高[1] TANG Ru-yue;LIU Chu-yue;FENG Xiao-gao(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2022年第3期271-275,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11701459)。

摘　　要：考虑如下极值问题:inf f∈ΛQ 1αf x^(2)+βf y^(2)J(z,f)/d x d y,α>0,β>0,其中Λ是矩形Q_(1)=[0,l]×[0,1]到矩形Q_(2)=[0,L]×[0,1]并保持端点对应的有限偏差的集合。同时借助经典的面积长度方法和平均值不等式方法分别证明了仿射拉伸变换为该极值问题的解。该结果推广了Astala等的结果。This paper mainly considers the extremal problem of inf f∈ΛQ 1αf x^(2)+βf y^(2)J(z,f)d x d y,α>0,β>0,among whichΛis the set of homeomorphic maps f from rectangle Q_(1)=[0,l]×[0,1]to rectangle Q_(2)=[0,L]×[0,1]with finite distortion.At the same time,the affine transformation is proved to be the solution of the extremal problem by classical area-length method and average value inequality.The result has generalized the result of Astala,Iwaniec,Martin and Onninen.

关 键 词：组合偏差函数 仿射拉伸变换 面积长度方法 拟共形映射 组合能量 

分 类 号：O174[理学—数学]