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Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow. (English) Zbl 1370.26014

MSC:
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:
[1] L. AMBROSIO - N. FUSCO - D. PALLARA, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000. Zbl0957.49001 MR1857292 · Zbl 0957.49001
[2] L. AMBROSIO, Transport equation and Cauchy problem for BV vector fields. Inventiones Mathematicae, 158 (2004), pp. 227-260. Zbl1075.35087 MR2096794 · Zbl 1075.35087
[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). · Zbl 1075.35087
[4] L. AMBROSIO - J. MALÝ, Very weak notions of differentiability. Preprint, 2005 (available at http://cvgmt.sns.it). MR2332676 · Zbl 1167.26001
[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. Zbl0865.35032 MR1411988 · Zbl 0865.35032
[6] F. COLOMBINI- N. LERNER, Uniqueness of continuous solutions for BV vector fields. Duke Math. J., 111 (2002), pp. 357-384. Zbl1017.35029 MR1882138 · Zbl 1017.35029
[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. Zbl1170.35364 MR2044334 · Zbl 1170.35364
[8] R. J. DI PERNA - P. L. LIONS: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), pp. 511-547. Zbl0696.34049 MR1022305 · Zbl 0696.34049
[9] H. FEDERER, Geometric Measure Theory. Springer, 1969. Zbl0176.00801 MR257325 · Zbl 0176.00801
[10] N. LERNER: Transport equations with partially BV velocities. Preprint, 2004. Zbl1170.35362 MR2124585 · Zbl 1170.35362
[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. Zbl0919.34028 MR1648524 · Zbl 0919.34028
[12] E. M. STEIN: Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Zbl0207.13501 MR290095 · Zbl 0207.13501
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