Pairings between measures and bounded functions and compensated compactness

Abstract

For all vectorfields ψ ε L∞(Ω, Rn) whose divergence is in Ln(Ω) and for all vector measures Μ in Ω whose curl is a measure we define a real valued measure (ψ, Μ) in Ω, that can be considered a suitable generalization of the scalar product of ψ and Μ. Several properties of the pairing (ψ, Μ) are then obtained. © 1983 Fondazione Annali di Matematica Pura ed Applicata.