加权全能量最小的圆环形变  

Deformation of Annuli with Smallest Total Weighted Energy

作　　者：张琴 冯小高[1] ZHANG Qin;FENG Xiaogao(College of Mathematics and Information,China West Normal University,Nan-chong 637009,Sichuan,China;College of Mathematics and Information,China West Normal University,Nanchong 637009,Sichuan,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：《数学年刊（A辑）》2022年第4期387-398,共12页Chinese Annals of Mathematics

基　　金：自然科学基金(No.11701459);西华师范大学科研启动项目(No.17E088)的资助。

摘　　要：主要考虑如下加权全能量极值问题:h∈■^(inf)(A_(1),A_(2))α∫∫A_(1)(|h_(N)|^(2)+|h_(T)|^(2))1/(|h_(z)|^(2))dz+β∫∫A_(1)|h_(N)|^(2)+|h_(T)|^(2)/J(z,h)1/|z|^(2)dz,其中■(A_(1),A_(2))代表从圆环A_(1)到圆环A_(2)的所有保向同胚映射的集合.研究得到唯一的极值映射为径向拉伸映射.这将[Iwaniec T,Onninen J.Hyperelastic deformations of smallest total energy[J].Arch Rational Mech Anal,2009,194:927-986.]的结果推广至非欧情形.同时,也分别研究了圆环上的加权调和能量的极值问题与加权偏差的极值问题.In this paper,the authors mainly study the following extremal problem for total weighted energy h∈■^(inf)(A_(1),A_(2))α∫∫A_(1)(|h_(N)|^(2)+|h_(T)|^(2))1/(|h_(z)|^(2))dz+β∫∫A_(1)|h_(N)|^(2)+|h_(T)|^(2)/J(z,h)1/|z|^(2)dz,where the class■(A_(1),A_(2))consists of orientation preserving homeomorphisms between annuli A_(1)and A_(2).They get that the unique extremal mapping is a certain radial mapping.This extends the result of[Iwaniec,T.and Onninen,J.,Hyperelastic deformations of smallest total energy,Arch.Rational Mech.Anal.,2009,vol.194,pp.927-986]to non-Euclidean version.Meanwhile,they also consider the extremal problems for weighted harmonic energy and weighted distortion on annuli,respectively.

关 键 词：加权全能量 加权调和能量 加权偏差 ODE 

分 类 号：O174.55[理学—数学]