Estimates and regularity results for the DiPerna-Lions flow

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 616, 2008, Pages 15-46

  Crippa, Gianluca ^a   De Lellis, Camillo ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44949219227     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2008.016     Document Type: Article

References (12)

1. Ambrosio, L., Transport equation and Cauchy problem for BV vector fields, Invent. Math. 158 (2004), 227-260.
2. Ambrosio, L., Transport equation and Cauchy problem for non-smooth vector fields, Lecture notes of the CIME course given in Cetraro, June 27-July 2, 2005.
3. Ambrosio, L., Crippa, G., Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields, Lecture notes of the Unione Matematica Italiana, Springer Verlag, to appear.
4. Ambrosio, L., De Lellis, C., Malý, J., On the chain rule for the divergence of vector fields: applications, partial results, open problems, Perspectives in Nonlinear Partial Differential Equations: in honor of Haim Brezis, to appear.
5. Ambrosio, L., Lecumberry, M., Maniglia, S., Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow, Rend. Sem. Mat. Univ. Padova 114 (2005), 29-50.
6. Bressan, A., An ill posed Cauchy problem for a hyperbolic system in two space dimensions, Rend. Sem. Mat. Univ. Padova 110 (2003), 103-117.
7. Bressan, A., A lemma and a conjecture on the cost of rearrangements, Rend. Sem. Mat. Univ. Padova 110 (2003), 97-102.
8. De Lellis, C., Notes on hyperbolic systems of conservation laws and transport equations, Handbook of differential equations, Evolutionary equations, Vol. 3 (2007).
9. DiPerna, R. J., Lions, P. L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547.
10. Federer, H., Geometric measure theory, Springer, 1969.
11. Lions, P. L., Mathematical topics in fluid mechanics, Vol. I: incompressible models, Oxford Lect. Ser. Math. Appl. 3 (1996).
12. Stein, E. M., Singular integrals and differentiability properties of functions, Princeton University Press, 1970.