# A chain rule formula in BV and applications to conservation laws

created by decicco on 05 Nov 2010
modified on 15 Dec 2012

[BibTeX]

Published Paper

Inserted: 5 nov 2010
Last Updated: 15 dec 2012

Journal: SIAM Journal on Mathematical Analysis
Year: 2011

Abstract:

In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to\R^d$ has bounded variation, $B(x,\cdot)$ is continuously differentiable and $B(\cdot,u)$ has bounded variation. We propose an application of this formula in order to deal in an intrinsic way the discontinuous flux appearing in conservation laws in one space variable.