On the chain rule formulas for divergences and applications to conservation laws
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.