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

The purpose of this paper is to study the lower semicontinuity with respect to the strong L1-convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, we prove that, if u∈SBD(Ω), (uh)⊂SBD(Ω) converges to u strongly in L1(Ω,Rn) and the measures |Ejuh| converge weakly * to a measure ν singular with respect to the Lebesgue measure, then∫Ωf(x,Eu)dx⩽liminfh→∞∫Ωf(x,Euh)dxprovided the integrand f satisfies a weak convexity property and standard growth assumptions of order p>1.