Calculus of Variations and Geometric Measure Theory
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G. Crasta - V. De Cicco

On the chain rule formulas for divergences and applications to conservation laws

created by decicco on 05 Oct 2016
modified on 07 Nov 2017

[BibTeX]

Accepted Paper

Inserted: 5 oct 2016
Last Updated: 7 nov 2017

Journal: Nonlinear Analysis
Year: 2017

Abstract:

In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function v(x)=B(x,u(x)), where B(.,t) is a divergence--measure vector field and u is a function of bounded variation. As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux.


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