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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