Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21497
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.
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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|Item Type:||Book Section, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||BV functions, Renormalized solutions, Continuity equation, Chain rule|
|Deposited On:||11 Nov 2009 15:13|
|Last Modified:||27 Nov 2013 21:58|
|Publisher:||American Mathematical Society|
|Series Name:||Contemporary Mathematics|
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