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

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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.

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Authors and Affiliations

  1. School of Mathematical Science, Xuzhou Normal University, Xuzhou, 221116, China

    Zhong-xue Lü

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Xiao-ping Yang

  3. School of Science, Huzhou Teacher College, Huzhou, 313000, China

    Min-ling Zheng

Authors
  1. Zhong-xue Lü
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  2. Xiao-ping Yang
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  3. Min-ling Zheng
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Corresponding author

Correspondence to Zhong-xue Lü.

Additional information

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)

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Lü, Zx., Yang, Xp. & Zheng, Ml. A lower semicontinuity result for some integral functionals in the space SBD. Acta Math. Appl. Sin. Engl. Ser. 24, 297–304 (2008). https://doi.org/10.1007/s10255-005-5188-6

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  • DOI: https://doi.org/10.1007/s10255-005-5188-6

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