Sixth GAMM Seminar on Microstructures - Abstract

Kružík, Martin

Oscillations and concentrations in sequences of gradients and weak lower semicontinuity

We use a generalization of Young measures due to DiPerna and Majda to analyze oscillations and concentrations in sequences of gradients. Particularly, we give an explicit characterization of generalized Young measures generated by gradients. This is then used to obtain sequential weak lower semicontinuity results for integral functionals with integrands whose modulus is bounded by the p-th power. Our results clearly explain reasons for failure of sequential weak continuity of determinants when p equals the dimension.