Acta mathematica scientia,Series B
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Lü Zhongxue; Yang Xiaoping
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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
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Lü Zhongxue; Yang Xiaoping. A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)[J].Acta mathematica scientia,Series B, 2008, 28(4): 770-778.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(08)60078-8
http://121.43.60.238/sxwlxbB/EN/Y2008/V28/I4/770
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