Nonlinear commutators and Jacobians (Q1384978)

In this interesting survey article the phenomena of cancellation in some nonlinear differential and integral expressions are studied. In the first part the cancellation phenomena in various types of linear and nonlinear commutators are studied. The results here are basic commutator results and the BMO--\(H^{1}\) duality. In the second part the commutator estimates are used in proving the higher order integrability of Jacobians and wedge products, and in establishing the compensated compactness principle. The third section is devoted to recent advances and application of the theory of Jacobians.