TitleOn the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems.
Publication TypeJournal Article
Year of Publication2007
AuthorsAmbrosio L., De Lellis C., Maly J.
Secondary AuthorsBerestycki H, Bertsch M, Browder FE, Nirenberg L, Peletier L, Véron L
JournalPerspectives in nonlinear partial differential equations
PublisherAmerican Mathematical Society
Place PublishedProvidence, RI
Type of Articletransport equations
ISBN Number978-0-8218-4190-7
KeywordsBV functions, Chain rule, Continuity equation, Renormalized solutions

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


Perspectives in nonlinear partial differential equations, 31–67, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007.