Traces and fine properties of a BD class of vector fields and applications
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 527-561.
@article{AFST_2005_6_14_4_527_0,
     author = {Ambrosio, Luigi and Crippa, Gianluca and Maniglia, Stefania},
     title = {Traces and fine properties of a $BD$ class of vector fields and applications},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {527--561},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {4},
     year = {2005},
     mrnumber = {2188582},
     zbl = {1091.35007},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_4_527_0/}
}
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Ambrosio, Luigi; Crippa, Gianluca; Maniglia, Stefania. Traces and fine properties of a $BD$ class of vector fields and applications. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 527-561. http://www.numdam.org/item/AFST_2005_6_14_4_527_0/

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

[2] Alberti (G. ), Ambrosio (L.). - A geometrical approach to monotone functions in Rn. Math. Z., 230, p. 259-316 (1999). | MR | Zbl

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

[4] Ambrosio ( L.), Bouchut (F.), De Lellis (C.). - Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions . Comm. Partial Diff. Eq., 29, p. 1635-1651 (2004). | MR | Zbl

[5] Ambrosio ( L.), Coscia (A.), Dal Maso (G.). - Fine properties of functions in BD. Arch. Rat. Mech. Anal., 139, p. 201-238 (1997). | MR | Zbl

[6] Ambrosio ( L.), De Lellis (C.). - Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions . IMRN, 41, p. 2205-2220 (2003 ). | MR | Zbl

[7] Ambrosio (L. ) , De Lellis ( C.), Maly (J.). - On the chain rule for the divergence of BV like vector fields: applications, partial results, open problems. Preprint (2005).

[8] Ambrosio ( L.), Fusco (N.), Pallara (D.). - Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs (2000). | MR | Zbl

[9] Anzellotti ( G.). - Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura App. , 135, p. 293-318 (1983). | MR | Zbl

[10] Anzellotti ( G.). - The Euler equation for functionals with linear growth. Trans. Amer. Mat. Soc., 290, p. 483-501 (1985). | MR | Zbl

[11] Anzellotti ( G. ). - Traces of bounded vectorfields and the divergence theorem. Unpublished preprint (1983).

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

[13] Bouchut (F. ) , James ( F.). - One dimensional transport equation with discontinuous coefficients. Nonlinear Analysis , 32, p. 891-933 (1998). | MR | Zbl

[14] Bouchut (F. ) , James ( F.), Mancini (S.). - Uniqueness and weak stablity for multi-dimensional transport equations with one-sided Lipschitz coefficients . Ann. Scuola Normale Superiore di Pisa, Classe di Scienze , (5) 4, p. 1-25 (2005). | Numdam | MR | Zbl

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

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

[17] Chen (G.-Q. ), Frid ( H.). - Divergence-measure fields and conservation laws. Arch. Rational Mech. Anal., 147, p. 89-118 (1999). | MR | Zbl

[18] Chen (G.-Q. ), Frid ( H.).- Extended divergence-measure fields and the Euler equation of gas dynamics. Comm. Math. Phys. , 236, p. 251-280 (2003). | MR | Zbl

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

[20] Colombini ( F.), Lerner (N.). - Uniqueness of L°° solutions for a class of conormal BV vector fields. Geometric Analysis of PDE and Several Complex Variables, Contemp. Math., 368, p. 133-156 (2005). | Zbl

[21] Di Perna ( R.J.), Lions (P.L.). - Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. , 98, p. 511-547 (1989). | Zbl

[22] Evans (L.C. ) , Gariepy ( R.F.). - Lecture notes on measure theory and fine properties of functions, CRC Press (1992).

[23] Federer (H. ). - Geometric measure theory, Springer (1969). | MR | Zbl

[24] Keyfitz ( B.L.), Kranzer (H.C.). - A system of nonstrictly hyperbolic conservation laws arising in elasticity theory. Arch. Rational Mech. Anal., 72, p. 219-241 (1980). | MR | Zbl

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

[26] Petrova ( G.), Popov (B.). - Linear transport equation with discontinuous coefficients. Comm. PDE, 24, p. 1849-1873 (1999). | MR | Zbl

[27] Popaud (F. ), Rascle (M.). - Measure solutions to the liner multidimensional transport equation with non-smooth coefficients. Comm. PDE, 22, p. 337-358 (1997). | MR | Zbl

[28] Temam (R.). - Problèmes mathématiques en plasticité. Gauthier-Villars, Paris ( 1983). | Zbl

[29] Vasseur ( A.). - Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal., 160, p. 181-193 (2001). | MR | Zbl