A Lower Semicontinuity Result for Some Integral Functionals in the Space SBD  

作　　者：Zhong-xue Lu Xiao-ping Yang Min-ling Zheng 

机构地区：[1]School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China [2]School of Science, Nanjing University of Science and Technology, Nanjing 210094, China [3]School of Science, Huzhou Teacher College, Huzhou 313000, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第2期297-304,共8页应用数学学报（英文版）

基　　金：the Doctorial Programme Foundation of Education Ministry of China (No.20030288002);the National Natural Science Foundation of China(No.10771181);Natural Science Foundation of Jiangsu Higher Education Bureau.(NO.07KJD110206)

摘　　要：In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.

关 键 词：SBD space integral functionals lower semicontinuity 

分 类 号：O177[理学—数学]