| 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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