# The Ordinary Differential Equation with non-Lipschitz Vector Fields

Bollettino dell'Unione Matematica Italiana (2008)

- Volume: 1, Issue: 2, page 333-348
- ISSN: 0392-4041

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topCrippa, Gianluca. "The Ordinary Differential Equation with non-Lipschitz Vector Fields." Bollettino dell'Unione Matematica Italiana 1.2 (2008): 333-348. <http://eudml.org/doc/290485>.

@article{Crippa2008,

abstract = {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.},

author = {Crippa, Gianluca},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {6},

number = {2},

pages = {333-348},

publisher = {Unione Matematica Italiana},

title = {The Ordinary Differential Equation with non-Lipschitz Vector Fields},

url = {http://eudml.org/doc/290485},

volume = {1},

year = {2008},

}

TY - JOUR

AU - Crippa, Gianluca

TI - The Ordinary Differential Equation with non-Lipschitz Vector Fields

JO - Bollettino dell'Unione Matematica Italiana

DA - 2008/6//

PB - Unione Matematica Italiana

VL - 1

IS - 2

SP - 333

EP - 348

AB - 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.

LA - eng

UR - http://eudml.org/doc/290485

ER -

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