Geodesic
The Ordinary Differential Equation with non-Lipschitz Vector Fields
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 333-348

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this note we survey some recent results on the well-posedness of the ordinary differential equation with non-Lipschitz vector fields. We introduce the notion of regular Lagrangian flow, which is the right concept of solution in this framework. We present two different approaches to the theory of regular Lagrangian flows. The first one is quite general and is based on the connection with the continuity equation, via the superposition principle. The second one exploits some quantitative a-priori estimates and provides stronger results in the case of Sobolev regularity of the vector field. 
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     author = {Crippa, Gianluca},
     title = {The {Ordinary} {Differential} {Equation} with {non-Lipschitz} {Vector} {Fields}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {333--348},
     publisher = {mathdoc},
     volume = {Ser. 9, 1},
     number = {2},
     year = {2008},
     zbl = {1203.35162},
     mrnumber = {2424297},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a2/}
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Crippa, Gianluca. The Ordinary Differential Equation with non-Lipschitz Vector Fields. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 333-348. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a2/