Traces and fine properties of a class of vector fields and applications
Luigi Ambrosio; Gianluca Crippa; Stefania Maniglia
Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)
- Volume: 14, Issue: 4, page 527-561
- ISSN: 0240-2963
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topAmbrosio, Luigi, Crippa, Gianluca, and Maniglia, Stefania. "Traces and fine properties of a $BD$ class of vector fields and applications." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.4 (2005): 527-561. <http://eudml.org/doc/73657>.
@article{Ambrosio2005,
author = {Ambrosio, Luigi, Crippa, Gianluca, Maniglia, Stefania},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {finite deformation; DiPerna-Lions theory; bounded deformation},
language = {eng},
number = {4},
pages = {527-561},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Traces and fine properties of a $BD$ class of vector fields and applications},
url = {http://eudml.org/doc/73657},
volume = {14},
year = {2005},
}
TY - JOUR
AU - Ambrosio, Luigi
AU - Crippa, Gianluca
AU - Maniglia, Stefania
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
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 4
SP - 527
EP - 561
LA - eng
KW - finite deformation; DiPerna-Lions theory; bounded deformation
UR - http://eudml.org/doc/73657
ER -
References
top- [1] Alberti ( G. ). — Rank-one properties for derivatives of functions with bounded variation. Proc. Roy. Soc. Edinburgh Sect. A, 123, p. 239-274 (1993). Zbl0791.26008MR1215412
- [2] Alberti ( G. ), Ambrosio ( L.). — A geometrical approach to monotone functions in Rn. Math. Z., 230, p. 259-316 (1999). Zbl0934.49025MR1676726
- [3] Ambrosio ( L.). — Transport equation and Cauchy problem for BV vector fields. Invent. Math., 158, p. 227-260 (2004). Zbl1075.35087MR2096794
- [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). Zbl1072.35116MR2103848
- [5] Ambrosio ( L.), Coscia ( A.), Dal Maso ( G.). — Fine properties of functions in BD. Arch. Rat. Mech. Anal., 139, p. 201-238 (1997). Zbl0890.49019MR1480240
- [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 ). Zbl1061.35048MR2000967
- [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). Zbl0957.49001MR1857292
- [9] Anzellotti ( G.). — Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura App. , 135, p. 293-318 (1983). Zbl0572.46023MR750538
- [10] Anzellotti ( G.). — The Euler equation for functionals with linear growth. Trans. Amer. Mat. Soc., 290, p. 483-501 (1985). Zbl0611.49018MR792808
- [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). Zbl0979.35032MR1822415
- [13] Bouchut ( F. ) , James ( F.). — One dimensional transport equation with discontinuous coefficients. Nonlinear Analysis , 32, p. 891-933 (1998). Zbl0989.35130MR1618393
- [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). Zbl1170.35363MR2165401
- [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). Zbl1114.35123MR2033003
- [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). Zbl0865.35032MR1411988
- [17] Chen ( G.-Q. ), Frid ( H.). — Divergence-measure fields and conservation laws. Arch. Rational Mech. Anal., 147, p. 89-118 (1999). Zbl0942.35111MR1702637
- [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). Zbl1036.35125MR1981992
- [19] Colombini ( F.), Lerner ( N.). — Uniqueness of continuous solutions for BV vector fields. Duke Math. J., 111, p. 357-384 (2002). Zbl1017.35029MR1882138
- [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). Zbl1064.35033
- [21] Di Perna ( R.J.), Lions ( P.L.). — Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. , 98, p. 511-547 (1989). Zbl0696.34049
- [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). Zbl0176.00801MR257325
- [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). Zbl0434.73019MR549642
- [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). Zbl0919.34028
- [26] Petrova ( G.), Popov ( B.). — Linear transport equation with discontinuous coefficients. Comm. PDE, 24, p. 1849-1873 (1999). Zbl0992.35104MR1708110
- [27] Popaud ( F. ), Rascle ( M.). - Measure solutions to the liner multidimensional transport equation with non-smooth coefficients. Comm. PDE, 22, p. 337-358 (1997). Zbl0882.35026MR1434148
- [28] Temam ( R.). — Problèmes mathématiques en plasticité. Gauthier-Villars, Paris ( 1983). Zbl0547.73026
- [29] Vasseur ( A.). — Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal., 160, p. 181-193 (2001). Zbl0999.35018MR1869441
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