*Published Paper*

**Inserted:** 10 jan 2005

**Last Updated:** 2 jul 2013

**Journal:** Perspective in nonlinear partial differential equations

**Pages:** 31-67

**Year:** 2007

**Notes:**

To appear in the forthcoming book by the AMS series in contemporary mathematics ``Perspectives in Nonlinear Partial Differential Equations: in honor of Haim Brezis''

**Abstract:**

We discuss the problem of computing the distributional divergence of
a vector field of the form h(w)B, where $h$ is a smooth scalar function
and B is a BV vector field, knowing the distributional divergence of
all vector fields w_{iB,} where w_{i} are the components of w.

We present partial results on this problem, conjectures, and links with other problems related to the SBV regularity of solutions of Hamilton-Jacobi equations and systems of conservation laws, and a conjecture recently made by Bressan.

For the most updated version and eventual errata see the page

http:/www.math.uzh.ch*index.php?id=publikationen&key1=493*

**Keywords:**
BV functions, Chain Rule, Renormalized solutions, continuity equation