Calculus of Variations and Geometric Measure Theory
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E. Marconi

Differentiability properties of the flow of 2d autonomous vector fields

created by marconi on 19 Jan 2021



Inserted: 19 jan 2021
Last Updated: 19 jan 2021

Year: 2021


We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompressible and divergence-free vector fields, taking advantage in both cases of the underlying Hamiltonian structure. Finally we provide an example of an autonomous planar Sobolev divergence-free vector field, such that the corresponding regular Lagrangian flow has no bounded variation.


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