Bogdan Raiţă
Scuola Normale Superiore di Pisa, Pisa, Italy

The aim of this talk is to review old and new results concerning the interaction between nonlinearity and weak convergence of pde constrained sequences. This is a ubiquitous theme in the study of nonlinear pde, of which we will place special emphasis on problems with variational structure. We will review classical results in the study of weak (lower semi-) continuity of variational integrals, concerning A-quasiconvexity, compensated compactness, and null Lagrangians. We will conclude with new results pertaining primarily to concentration effects in weak convergence, which we used to answer questions of Coifman-Lions-Meyer-Semmes and De Philippis. Time permitting, we will express our results in the language of generalized Young measures (cf. Di Perna-Majda measures, defect measures). Joint work with A. Guerra and M. Schrecker.