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

doi:10.1016/S0252-9602(08)60078-8

Acta mathematica scientia,Series B

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

Lü Zhongxue; Yang Xiaoping

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

Abstract:

In this article, the authors obtain an integral representation for the relaxation of the functional
F(x, u, Ω):={∫_Ωf(x, u(x), εu(x))dx if u ∈ W^{1, 1}(Ω, R^N), +∞ 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

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

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