On the structure of diffuse measures for parabolic capacities.

Let Q = (0 , T) × Ω , where Ω is a bounded open subset of R d. We consider the parabolic p -capacity on Q naturally associated with the usual p -Laplacian. Droniou, Porretta, and Prignet have shown that if a bounded Radon measure μ on Q is diffuse, i.e. charges no set of zero p -capacity, p > 1 , then it is of the form μ = f + div (G) + g t for some f ∈ L 1 (Q) , G ∈ (L p ′ (Q)) d and g ∈ L p (0 , T ; W 0 1 , p (Ω) ∩ L 2 (Ω)). We show the converse of this result: if p > 1 , then each bounded Radon measure μ on Q admitting such a decomposition is diffuse. [ABSTRACT FROM AUTHOR]