Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - G. Crippa

Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields

created by ambrosio on 17 Jan 2006
modified by crippa on 05 Mar 2009

[BibTeX]

Published Paper

Inserted: 17 jan 2006
Last Updated: 5 mar 2009

Journal: In: Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana
Volume: 5
Year: 2008

Abstract:

In these notes we illustrate some recent developments of the DiPerna-Lions theory in the case of vector fields having a BV regularity with respect to the spatial variables. In the Sobolev case we discuss also the (weak) differentiability properties of the flow X(t,x) with respect to the x variable, and some recent quantitative regularity estimates leading to a new proof of the existence and the uniqueness of the flow, as well as to quantitative stability results.

Keywords: Flow theory, Approximate differentiability, Maximal functions


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