Inserted: 10 jan 2005
Last Updated: 2 jul 2013
Journal: Perspective in nonlinear partial differential equations
To appear in the forthcoming book by the AMS series in contemporary mathematics ``Perspectives in Nonlinear Partial Differential Equations: in honor of Haim Brezis''
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 wiB, where wi 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
Keywords: BV functions, Chain Rule, Renormalized solutions, continuity equation