Ricerc@Sapienza

We introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293-318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89-118], all the main properties and features (e.g.

In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function $\v(x)=\B(x,u(x))$,
where $\B(\cdot,t)$ is a divergence--measure vector field and $u$ is a function of bounded variation.
As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux.