@article{AFST_2005_6_14_4_527_0,
author = {Luigi Ambrosio and Gianluca Crippa and Stefania Maniglia},
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},
zbl = {1091.35007},
mrnumber = {2188582},
language = {en},
url = {https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_527_0/}
}
TY - JOUR AU - Luigi Ambrosio AU - Gianluca Crippa AU - Stefania Maniglia TI - Traces and fine properties of a $BD$ class of vector fields and applications JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2005 SP - 527 EP - 561 VL - 14 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_527_0/ LA - en ID - AFST_2005_6_14_4_527_0 ER -
%0 Journal Article %A Luigi Ambrosio %A Gianluca Crippa %A Stefania Maniglia %T Traces and fine properties of a $BD$ class of vector fields and applications %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2005 %P 527-561 %V 14 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_527_0/ %G en %F AFST_2005_6_14_4_527_0
Luigi Ambrosio; Gianluca Crippa; Stefania Maniglia. 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. https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_527_0/
[1] - Rank-one properties for derivatives of functions with bounded variation. Proc. Roy. Soc. Edinburgh Sect. A, 123, p. 239-274 (1993). | Zbl | MR
[2] , - A geometrical approach to monotone functions in Rn. Math. Z., 230, p. 259-316 (1999). | Zbl | MR
[3] - Transport equation and Cauchy problem for BV vector fields. Invent. Math., 158, p. 227-260 (2004). | Zbl | MR
[4] , , - Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions . Comm. Partial Diff. Eq., 29, p. 1635-1651 (2004). | Zbl | MR
[5] , , - Fine properties of functions in BD. Arch. Rat. Mech. Anal., 139, p. 201-238 (1997). | Zbl | MR
[6] , - Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions . IMRN, 41, p. 2205-2220 (2003 ). | Zbl | MR
[7] , , - On the chain rule for the divergence of BV like vector fields: applications, partial results, open problems. Preprint (2005).
[8] , , - Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs (2000). | Zbl | MR
[9] - Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura App. , 135, p. 293-318 (1983). | Zbl | MR
[10] - The Euler equation for functionals with linear growth. Trans. Amer. Mat. Soc., 290, p. 483-501 (1985). | Zbl | MR
[11] - Traces of bounded vectorfields and the divergence theorem. Unpublished preprint (1983).
[12] - Renormalized solutions to the Vlasov equation with coefficients of bounded variation. Arch. Rational Mech. Anal., 157, p. 75-90 (2001). | Zbl | MR
[13] , - One dimensional transport equation with discontinuous coefficients. Nonlinear Analysis , 32, p. 891-933 (1998). | Zbl | MR
[14] , , - 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). | Zbl | MR | Numdam
[15] - An ill posed Cauchy problem for a hyperbolic system in two space dimensions. Rend. Sem. Mat. Univ. Padova, 110, p. 103-117 (2003). | Zbl | MR | Numdam
[16] , - On some analogy between different approaches to first order PDE's with nonsmooth coefficients. Adv. Math. Sci Appl., 6, p. 689-703 (1996). | Zbl | MR
[17] , - Divergence-measure fields and conservation laws. Arch. Rational Mech. Anal., 147, p. 89-118 (1999). | Zbl | MR
[18] , - Extended divergence-measure fields and the Euler equation of gas dynamics. Comm. Math. Phys. , 236, p. 251-280 (2003). | Zbl | MR
[19] , - Uniqueness of continuous solutions for BV vector fields. Duke Math. J., 111, p. 357-384 (2002). | Zbl | MR
[20] , - 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] , - Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. , 98, p. 511-547 (1989). | Zbl
[22] , - Lecture notes on measure theory and fine properties of functions, CRC Press (1992).
[23] - Geometric measure theory, Springer (1969). | Zbl | MR
[24] , - A system of nonstrictly hyperbolic conservation laws arising in elasticity theory. Arch. Rational Mech. Anal., 72, p. 219-241 (1980). | Zbl | MR
[25] - Sur les équations différentielles ordinaires et les équations de transport. C. R. Acad. Sci. Paris Sér. I, 326, p. 833-838 (1998). | Zbl
[26] , - Linear transport equation with discontinuous coefficients. Comm. PDE, 24, p. 1849-1873 (1999). | Zbl | MR
[27] , - Measure solutions to the liner multidimensional transport equation with non-smooth coefficients. Comm. PDE, 22, p. 337-358 (1997). | Zbl | MR
[28] - Problèmes mathématiques en plasticité. Gauthier-Villars, Paris ( 1983). | Zbl
[29] - Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal., 160, p. 181-193 (2001). | Zbl | MR