A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)  

作　　者：吕中学 杨孝平 

机构地区：[1]School of Mathematical Science,Xuzhou Normal University [2]School of Sciences,Nanjing University of Science and Technology

出　　处：《Acta Mathematica Scientia》2008年第4期770-778,共9页数学物理学报（B辑英文版）

基　　金：the Doctorial Programme Foundation of EducationMinistry of of China(20030288002);the Science Foundation of Jiangsu Province(BK2006209);NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206);NNSF of China(10771181)

摘　　要：In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.

关 键 词：Integral representation RELAXATION special functions with bounded deformation 

分 类 号：O174[理学—数学]