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

Abstract

In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function $\mathbf{v}(x)=\mathbf{B}(x,u(x))$, where $\mathbf{B}(\cdot ,t)$ 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.

19 pages

References in corpus (3)

• Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux
• Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness
• A nonautonomous chain rule in $W^{1,p}$ and $BV$

Cited by in corpus (2)

• Anzellotti's pairing theory and the Gauss--Green theorem
• An extension of the pairing theory between divergence-measure fields and BV functions