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

Ambrosio, L; De Lellis, C; Malý, J (2007). *On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems.* In: Berestycki, H; Bertsch, M; Browder, F E; Nirenberg, L; Peletier, L; Véron, L. Perspectives in nonlinear partial differential equations. Providence, RI: American Mathematical Society , 31-67.

## 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

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## Additional indexing

Item Type: | Book Section, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | BV functions, Renormalized solutions, Continuity equation, Chain rule |

Language: | English |

Date: | 2007 |

Deposited On: | 11 Nov 2009 15:13 |

Last Modified: | 05 Apr 2016 13:23 |

Publisher: | American Mathematical Society |

Series Name: | Contemporary Mathematics |

Number: | 446 |

ISSN: | 0271-4132 |

ISBN: | 978-0-8218-4190-7 |

Official URL: | http://www.ams.org/bookstore-getitem/item=CONM-446 |

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