Lipschitz regularity and approximate differentiability of the Diperna-Lions flow

Luigi Ambrosio; Myriam Lecumberry; Stefania Maniglia

Rendiconti del Seminario Matematico della Università di Padova (2005)

  • Volume: 114, page 29-50
  • ISSN: 0041-8994

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Ambrosio, Luigi, Lecumberry, Myriam, and Maniglia, Stefania. "Lipschitz regularity and approximate differentiability of the Diperna-Lions flow." Rendiconti del Seminario Matematico della Università di Padova 114 (2005): 29-50. <http://eudml.org/doc/108667>.

@article{Ambrosio2005,
author = {Ambrosio, Luigi, Lecumberry, Myriam, Maniglia, Stefania},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {29-50},
publisher = {Seminario Matematico of the University of Padua},
title = {Lipschitz regularity and approximate differentiability of the Diperna-Lions flow},
url = {http://eudml.org/doc/108667},
volume = {114},
year = {2005},
}

TY - JOUR
AU - Ambrosio, Luigi
AU - Lecumberry, Myriam
AU - Maniglia, Stefania
TI - Lipschitz regularity and approximate differentiability of the Diperna-Lions flow
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2005
PB - Seminario Matematico of the University of Padua
VL - 114
SP - 29
EP - 50
LA - eng
UR - http://eudml.org/doc/108667
ER -

References

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  1. [1] L. AMBROSIO - N. FUSCO - D. PALLARA, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000. Zbl0957.49001MR1857292
  2. [2] L. AMBROSIO, Transport equation and Cauchy problem for BV vector fields. Inventiones Mathematicae, 158 (2004), pp. 227-260. Zbl1075.35087MR2096794
  3. [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). Zbl1075.35087
  4. [4] L. AMBROSIO - J. MALÝ, Very weak notions of differentiability. Preprint, 2005 (available at http://cvgmt.sns.it). Zbl1167.26001MR2332676
  5. [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. Zbl0865.35032MR1411988
  6. [6] F. COLOMBINI- N. LERNER, Uniqueness of continuous solutions for BV vector fields. Duke Math. J., 111 (2002), pp. 357-384. Zbl1017.35029MR1882138
  7. [7] C. LE BRIS - P. L. LIONS, Renormalized solutions of some transport equations with partially W1;1 velocities and applications. Annali di Matematica, 183 (2003), pp. 97-130. Zbl1170.35364MR2044334
  8. [8] R. J. DI PERNA - P. L. LIONS: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), pp. 511-547. Zbl0696.34049MR1022305
  9. [9] H. FEDERER, Geometric Measure Theory. Springer, 1969. Zbl0176.00801MR257325
  10. [10] N. LERNER: Transport equations with partially BV velocities. Preprint, 2004. Zbl1170.35362MR2124585
  11. [11] P. L. LIONS, Sur les équations différentielles ordinaires et les équations de transport. C. R. Acad. Sci. Paris Sér. I, 326 (1998), pp. 833-838. Zbl0919.34028MR1648524
  12. [12] E. M. STEIN: Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Zbl0207.13501MR290095

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