First General Lower Semicontinuity and Relaxation Results for Strong Materials

We consider the case of strong materials, i.e. the situation where the growth of integrands from below guarantees the lack of discontinuities for deformations with finite energy. We show that, in this case, both lower semicontinuity and relaxation results relay on the a.e. differentiability property of admissible deformations and on the uniform convergence of weakly convergent sequences bounded in energy.