A lower semicontinuity result for some integral functionals in the space SBD期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A lower semicontinuity result for some integral functionals in the space SBD

Authors:

Zhong-xue Lü Xiao-ping Yang Min-ling Zheng

Institution:

[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

Abstract:

In this paper, we obtain a lower semicontinuity result with respect to the strong L ¹-convergence of the integral functionals

$F(u,\Omega ) = \int\limits_\Omega {f(x,u(x),\varepsilon u(x))dx}$

defined in the space SBD of special functions with bounded deformation. Here ɛu 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. Supported the Doctorial Programme Foundation of Education Ministry of China.(No.20030288002) and the National Natural Science Foundation of China (No. 10771181) and Natural Science Foundation of Jiangsu Higher Education Bureau. (NO. 07KJD110206)

Keywords:

SBD space integral functionals lower semicontinuity

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