Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow

Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

Volumn 114, Issue , 2005, Pages 29-50

  Ambrosio, Luigi ^a   Lecumberry, Myriam ^b   Maniglia, Stefania ^c  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247518966     PISSN: 00418994     EISSN: 22402926     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

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2. L. Ambrosio, Transport equation and Cauchy problem for BV vector fields. Inventiones Mathematicae, 158 (2004), pp. 227-260.
3. L. Ambrosio, Lecture notes on transport equation and Cauchy problem for BV vector fields and applications. Preprint, 2004 (available at http://cvgmt.sns.it).
4. L. Ambrosio-J. Malý, Very weak notions of differentiability. Preprint, 2005 (available at http://cvgmt.sns.it).
5. 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), pp. 689-703.
6. F. Colombini-N. Lerner, Uniqueness of continuous solutions for BV vector fields. Duke Math. J., 111 (2002), pp. 357-384.
7. 1,1 velocities and applications. Annali di Matematica, 183 (2003), pp. 97-130.
8. R. J. Di Perna-P. L. Lions: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), pp. 511-547.
9. H. Federer, Geometric Measure Theory. Springer, 1969.
10. N. Lerner: Transport equations with partially BV velocities. Preprint, 2004.
11. P. L. Lions, Sur les équations différentielles ordinaires et les équations de transport. C. R. Acad. Sci. Paris SÝr. I, 326 (1998), pp. 833-838.
12. E. M. Stein: Singular integrals and differentiability properties of functions. Princeton University Press, 1970.