Compensated compactness

Compensated compactness is the principle that certain bilinear or nonlinear operators may exhibit good boundedness properties (e.g. mapping bounded sequences to precompact sequences in a suitable strong topology) if they exhibit some cancellation in their internal structure. It is of particular importance in conservation law equations. For nonlinear dispersive and wave equations, the counterpart of this principle appears to be the null form estimates. See also concentration compactness, which is another way of salvaging a type of compactness from a non-compact situation.