Summary
For all vectorfields ψ ε L∞(Ω,R n) 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.
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Anzellotti, G. Pairings between measures and bounded functions and compensated compactness. Annali di Matematica pura ed applicata 135, 293–318 (1983). https://doi.org/10.1007/BF01781073
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DOI: https://doi.org/10.1007/BF01781073