Title On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems. Publication Type Journal Article Year of Publication 2007 Authors Ambrosio L., De Lellis C., Maly J. Secondary Authors Berestycki H, Bertsch M, Browder FE, Nirenberg L, Peletier L, Véron L Journal Perspectives in nonlinear partial differential equations Volume 446 Pagination 31–67 Publisher American Mathematical Society Place Published Providence, RI Type of Article transport equations ISSN 0271-4132 ISBN Number 978-0-8218-4190-7 Keywords BV functions, Chain rule, Continuity equation, Renormalized solutions 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 Notes Perspectives in nonlinear partial differential equations, 31–67, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007. URL http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.8482
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