Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]
Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 972, 29 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl
De Lellis, Camillo. Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions], dans Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 972, 29 p.. http://geodesic.mathdoc.fr/item/AST_2008__317__175_0/
@incollection{AST_2008__317__175_0,
     author = {De Lellis, Camillo},
     title = {Ordinary differential equations with rough coefficients and the renormalization theorem of {Ambrosio} [after {Ambrosio,} {DiPerna,} {Lions]}},
     booktitle = {S\'eminaire Bourbaki - Volume 2006/2007  - Expos\'es 967-981},
     series = {Ast\'erisque},
     note = {talk:972},
     pages = {175--203},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     mrnumber = {2487734},
     zbl = {1169.35060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AST_2008__317__175_0/}
}
TY  - CHAP
AU  - De Lellis, Camillo
TI  - Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]
BT  - Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981
AU  - Collectif
T3  - Astérisque
N1  - talk:972
PY  - 2008
SP  - 175
EP  - 203
IS  - 317
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_2008__317__175_0/
LA  - en
ID  - AST_2008__317__175_0
ER  - 
%0 Book Section
%A De Lellis, Camillo
%T Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]
%B Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981
%A Collectif
%S Astérisque
%Z talk:972
%D 2008
%P 175-203
%N 317
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_2008__317__175_0/
%G en
%F AST_2008__317__175_0

[1] M. Aizenman - "On vector fields as generators of flows: a counterexample to Nelson's conjecture", Ann. Math. (2) 107 (1978), p. 287-296. | MR | Zbl | DOI

[2] G. Alberti - "Rank one property for derivatives of functions with bounded variation", Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), p. 239-274. | MR | Zbl | DOI

[3] G. Alberti, S. Bianchini & C. Gianluca - In préparation.

[4] L. Ambrosio - "Lecture notes on transport equation and Cauchy problem for bv vector fields and applications", Lectures of a course given in Luminy, October 2003.

[5] L. Ambrosio, "Transport equation and Cauchy problem for non-smooth vector fields", Lecture Notes of the CIME Summer school in Cetrary, June 27-July 2, 2005. | Zbl | MR

[6] L. Ambrosio, "Transport equation and Cauchy problem for BV vector fields", Invent. Math. 158 (2004), p. 227-260. | MR | Zbl | DOI

[7] L. Ambrosio, F. Bouchut & C. De Lellis - "Well-posedness for a class of hyperbolic systemes of conservation laws in several space dimensions", Comm. Partial Differential Equations 29 (2004), p. 1635-1651. | MR | Zbl | DOI

[8] L. Ambrosio & G. Crippa - "Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields", in Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana, Springer Verlag, Berlin-Heidelberg, 2008. | MR | Zbl | DOI

[9] L. Ambrosio, G. Crippa & S. Maniglia - "Traces and fine properties of a BD class of vector fields and applications", Ann. Fac. Sci. Toulouse Math. (6) 14 (2005), p. 527-561. | MR | Zbl | EuDML | Numdam | DOI

[10] L. Ambrosio & C. De Lellis - "Existence of solutions for a class of hyperbolic Systems of conservation laws in several space dimensions", Int. Math. Res. Not. 41 (2003), p. 2205-2220. | MR | Zbl | DOI

[11] L. Ambrosio, C. De Lellis & J. Maly - "On the chain rule for the divergence of vector fields: applications, partial results, open problems", in Perspectives in nonlinear partial differential équations, 2007, p. 31-67, | MR | Zbl | DOI

[11] L. Ambrosio, C. De Lellis & J. Maly - "On the chain rule for the divergence of vector fields: applications, partial results, open problems", Contemp. Math. 446, Amer. Math. Soc., Providence, RI. | MR | Zbl

[12] L. Ambrosio, N. Fusco & D. Pallara - Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, 2000. | MR | Zbl

[13] L. Ambrosio, M. Lecumberry & S. Maniglia - "Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow", Rend. Sem. Mat. Univ. Padova 114 (2005), p. 29-50 (2006). | MR | EuDML | Zbl | Numdam

[14] L. Ambrosio & J. Malý - "Very weak notions of differentiability", Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), p. 447-455. | MR | Zbl | DOI

[15] F. Bouchut - "Renormalized solutions to the Vlasov equation with coefficients of bounded variation", Arch. Ration. Mech. Anal. 157 (2001), p. 75-90. | MR | Zbl | DOI

[16] F. Bouchut & L. Desvillettes - "On two-dimensional Hamiltonian transport equations with continuous coefficients", Differential Intégral Equations 14 (2001), p. 1015-1024. | MR | Zbl

[17] A. Bressan - "An ill posed Cauchy problem for a hyperbolic System in two space dimensions", Rend. Sem. Mat. Univ. Padova 110 (2003), p. 103-117. | MR | Zbl | EuDML | Numdam

[18] A. Bressan, "A lemma and a conjecture on the cost of rearrangements", Rend. Sem. Mat. Univ. Padova 110 (2003), p. 97-102. | MR | Zbl | EuDML | Numdam

[19] I. Capuzzo Dolcetta & B. Perthame - "On some analogy between different approaches to first order PDE's with nonsmooth coefficients", Adv. Math. Sci. Appl. 6 (1996), p. 689-703. | MR | Zbl

[20] F. Colombini, G. Crippa & J. Rauch - "A note on two-dimensional transport with bounded divergence", Comm. Partial Differential Equations 31 (2006), p. 1109-1115. | MR | Zbl | DOI

[21] F. Colombini & N. Lerner - "Uniqueness of continuous solutions for BV vector fields", Duke Math. J. 111 (2002), p. 357-384. | MR | Zbl | DOI

[22] F. Colombini, T. Luo & J. Rauch - "Uniqueness and nonuniqueness for nonsmooth divergence free transport", in Séminaire: Équations aux Dérivées Partielles, 2002-2003, Sémin. Équ. Dériv. Partielles, École polytech., 2003, p. 21. | MR | Zbl | EuDML | Numdam

[23] G. Crippa & C. De Lellis - "Oscillatory solutions to transport equations", Indiana Univ. Math. J. 55 (2006), p. 1-13. | MR | Zbl | DOI

[24] G. Crippa & C. De Lellis, "Estimates and regularity results for the DiPerna-Lions flow", J. reine angew. Math. 616 (2008), p. 15-46. | MR | Zbl

[25] C. De Lellis - "Notes on hyperbolic Systems of conservation laws and transport equations", Handbook of evolutionary differential équations, Vol. III, 2006. | MR | Zbl

[26] C. De Lellis, "A note on Alberti's rank-one theorem", in Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana, Springer Verlag, Berlin-Heidelberg, 2008. | MR | Zbl | DOI

[27] N. Depauw - "Non-unicité du transport par un champ de vecteurs presque BV", in Séminaire: Équations aux Dérivées Partielles, 2002-2003, Sémin. Equ. Dériv. Partielles, École polytech., 2003, p. 9. | MR | Zbl | EuDML | Numdam

[28] R. J. Diperna & P.-L. Lions - "Ordinary differential equations, transport theory and Sobolev spaces", Invent. Math. 98 (1989), p. 511-547. | MR | Zbl | EuDML | DOI

[29] L. C. Evans - Partial differential equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, 1998. | MR | Zbl

[30] L. C. Evans & R. F. Gariepy - Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, 1992. | MR | Zbl

[31] M. Hauray - "On two-dimensional Hamiltonian transport equations with L l o c p coefficients", Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), p. 625-644. | MR | Zbl | EuDML | Numdam | DOI

[32] C. Le Bris & P.-L. Lions - "Renormalized solutions of some transport equations with partially W 1,1 velocities and applications", Ann. Mat. Pura Appl. (4) 183 (2004), p. 97-130. | MR | Zbl | DOI

[33] P.-L. Lions - "Sur les équations différentielles ordinaires et les équations de transport", C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), p. 833-838. | MR | Zbl | DOI