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

The purpose of this paper is to study the lower semicontinuity with respect to the strong L1L1-convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, we prove that, if u∈SBD(Ω)u∈SBD(Ω), (uh)⊂SBD(Ω)(uh)⊂SBD(Ω) converges to u strongly in L1(Ω,Rn)L1(Ω,Rn) and the measures |Ejuh||Ejuh| converge weakly ** to a measure νν singular with respect to the Lebesgue measure, then View the MathML source∫Ωf(x,Eu)dx⩽liminfh→∞∫Ωf(x,Euh)dx Turn MathJax on provided the integrand f satisfies a weak convexity property and standard growth assumptions of order p>1p>1.