Calculus of Variations and Geometric Measure Theory
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F. Bouchut - G. Crippa

Lagrangian flows for vector fields with gradient given by a singular integral

created by crippa on 21 Aug 2012
modified on 08 Sep 2014


Published Paper

Inserted: 21 aug 2012
Last Updated: 8 sep 2014

Journal: J. Hyper. Differential Equations
Volume: 10
Number: 2
Pages: 235-282
Year: 2013


We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an $L^1$ function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the $BV$ theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations.


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