Acta mathematica scientia,Series B

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

Lü Zhongxue; Yang Xiaoping   

  1. School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China; School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China
  • Received:2006-08-23 Revised:1900-01-01 Online:2008-10-20 Published:2008-10-20
  • Contact: Yang Xiaoping

Abstract:

In this article, the authors obtain an integral representation for the relaxation of the functional
F(x, u, Ω):={∫Ω f(x, u(x), εu(x))dx if u ∈ W1, 1(Ω, RN), +∞ otherwise,
in the space of functions of bounded deformation, with respect to L1-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption.

Key words: Integral representation, relaxation, special functions with bounded deformation

CLC Number: 

  • 49J10
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