Title: On the compensated compactness
method for concentration effects
Abstract: We present some new and surprising
examples of uniform integrability of sequences satisfying
both a linear pde constraint and a (nonlinear) pointwise
constraint. One example that we will explore would be
higher integrability of hessian sequences that does not
follow from the theory of quasiregular mappings. Earlier
examples can be found in the works of D. Serre and G. De
Philippis et al. We identify a new phenomenon that gives a
counterexample to a conjecture in G. De Philippis et al.
Some of our proofs rely on the theory of k-hessian
equations. This is joint work with A. Guerra and M.
Schrecker.