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 bound...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.展开更多
基金the Doctorial Programme Foundation of EducationMinistry of of China(20030288002)the Science Foundation of Jiangsu Province(BK2006209)+1 种基金NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206)NNSF of China(10771181)
文摘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.