Some remarks on the continuity equation

Patrick Bernard[1]

  • [1] Université Paris-Dauphine, CEREMADE, UMR CNRS 7534 Pl. du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France

Séminaire Équations aux dérivées partielles (2008-2009)

  • Volume: 2008-2009, page 1-12

Abstract

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This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.

How to cite

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Bernard, Patrick. "Some remarks on the continuity equation." Séminaire Équations aux dérivées partielles 2008-2009 (2008-2009): 1-12. <http://eudml.org/doc/11202>.

@article{Bernard2008-2009,
abstract = {This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.},
affiliation = {Université Paris-Dauphine, CEREMADE, UMR CNRS 7534 Pl. du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France},
author = {Bernard, Patrick},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Borel map; generic uniqueness},
language = {eng},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Some remarks on the continuity equation},
url = {http://eudml.org/doc/11202},
volume = {2008-2009},
year = {2008-2009},
}

TY - JOUR
AU - Bernard, Patrick
TI - Some remarks on the continuity equation
JO - Séminaire Équations aux dérivées partielles
PY - 2008-2009
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2008-2009
SP - 1
EP - 12
AB - This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.
LA - eng
KW - Borel map; generic uniqueness
UR - http://eudml.org/doc/11202
ER -

References

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  2. L. Ambrosio : Transport equation and Cauchy problem for non-smooth vector fields. Lecture Notes in Mathematics “Calculus of Variations and Non-Linear Partial Differential Equations” (CIME Series, Cetraro, 2005) 1927, B. Dacorogna, P. Marcellini eds., 2–41, 2008. Zbl1159.35041MR2408257
  3. L. Ambrosio, G. Crippa : Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. UMI Lecture Notes, Springer, in press. Zbl1155.35313
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  5. L. Ambrosio and P. Bernard : Uniqueness of signed measures solving the continuity equation for Osgood vector fields, Rendiconti Lincei - Mat. e App. (RLM) 19 (2008) no 3. , 237-245. Zbl1204.35069MR2439520
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  15. S. Maniglia : Probabilistic representation and uniqueness results for measure-valued solutions of transport equations. J. Math. Pures Appl.87 (2007), 601–626. Zbl1123.60048MR2335089
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