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Volumn 158, Issue 2, 2004, Pages 227-260

Transport equation and Cauchy problem for BV vector fields

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EID: 7544243351     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0367-2     Document Type: Article
Times cited : (659)

References (34)
  • 1
    • 0141580734 scopus 로고
    • On vector fields as generators of flows: A counterexample to Nelson's conjecture
    • Aizenman, M.: On vector fields as generators of flows: a counterexample to Nelson's conjecture. Ann. Math. 107, 287-296 (1978)
    • (1978) Ann. Math. , vol.107 , pp. 287-296
    • Aizenman, M.1
  • 2
    • 84971972568 scopus 로고
    • Rank-one properties for derivatives of functions with bounded variation
    • Alberti, G.: Rank-one properties for derivatives of functions with bounded variation. Proc. R. Soc. Edinb., Sect. A, Math. 123, 239-274 (1993)
    • (1993) Proc. R. Soc. Edinb., Sect. A, Math. , vol.123 , pp. 239-274
    • Alberti, G.1
  • 4
    • 0012520952 scopus 로고    scopus 로고
    • A new approach to variational problems with multiple scales
    • Alberti, G., Müller, S.: A new approach to variational problems with multiple scales. Commun. Pure Appl. Math. 54, 761-825 (2001)
    • (2001) Commun. Pure Appl. Math. , vol.54 , pp. 761-825
    • Alberti, G.1    Müller, S.2
  • 5
    • 7544247248 scopus 로고    scopus 로고
    • Personal communication
    • Alberti, G.: Personal communication
    • Alberti, G.1
  • 7
    • 7544251770 scopus 로고    scopus 로고
    • On the rectifiability of defect measures arising in a micromagnetics model
    • in honor of O.A. Ladyzhenskaya, ed. by M.S. Birman, S. Hildebrandt, V.A. Solonnikov and N. Uraltseva. International Mathematical Series, Kluwer/Plenum
    • Ambrosio, L., Kirchheim, B., Lecumberry, M., Riviere, T.: On the rectifiability of defect measures arising in a micromagnetics model. Nonlinear Problems in Mathematical Physics and related topics II, in honor of O.A. Ladyzhenskaya, ed. by M.S. Birman, S. Hildebrandt, V.A. Solonnikov and N. Uraltseva pp. 29-60. International Mathematical Series, Kluwer/Plenum 2002
    • (2002) Nonlinear Problems in Mathematical Physics and Related Topics , vol.2 , pp. 29-60
    • Ambrosio, L.1    Kirchheim, B.2    Lecumberry, M.3    Riviere, T.4
  • 8
    • 0141575636 scopus 로고    scopus 로고
    • Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions
    • Ambrosio, L., De Lellis, C.: Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions. Int. Math. Res. Not. 41, 2205-2220 (2003)
    • (2003) Int. Math. Res. Not. , vol.41 , pp. 2205-2220
    • Ambrosio, L.1    De Lellis, C.2
  • 9
    • 10844284704 scopus 로고    scopus 로고
    • Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions
    • Preprint 2003 (submitted to)
    • Ambrosio, L., Bouchut, F., De Lellis, C.: Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. Preprint 2003 (submitted to Comm. PDE and available at http://cvgmt.sns.it)
    • Comm. PDE
    • Ambrosio, L.1    Bouchut, F.2    De Lellis, C.3
  • 10
    • 0032187452 scopus 로고    scopus 로고
    • Weak solutions for the semigeostrophic equation formulated as a couples Monge-Ampere transport problem
    • Benamou, J.-D., Brenier, Y.: Weak solutions for the semigeostrophic equation formulated as a couples Monge-Ampere transport problem. SIAM J. Appl. Math. 58, 1450-1461 (1998)
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1450-1461
    • Benamou, J.-D.1    Brenier, Y.2
  • 11
    • 0032092187 scopus 로고    scopus 로고
    • One dimensional transport equation with discontinuous coefficients
    • Bouchut, F., James, F.: One dimensional transport equation with discontinuous coefficients. Nonlinear Anal. 32, 891-933 (1998)
    • (1998) Nonlinear Anal. , vol.32 , pp. 891-933
    • Bouchut, F.1    James, F.2
  • 12
    • 0035627821 scopus 로고    scopus 로고
    • Renormalized solutions to the Vlasov equation with coefficients of bounded variation
    • Bouchut, F.: Renormalized solutions to the Vlasov equation with coefficients of bounded variation. Arch. Ration. Mech. Anal. 157, 75-90 (2001)
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , pp. 75-90
    • Bouchut, F.1
  • 14
    • 0000563828 scopus 로고    scopus 로고
    • On some analogy between different approaches to first order PDE's with nonsmooth coefficients
    • Capuzzo Dolcetta, I., Perthame, B.: On some analogy between different approaches to first order PDE's with nonsmooth coefficients. Adv. Math. Sci. Appl. 6, 689-703 (1996)
    • (1996) Adv. Math. Sci. Appl. , vol.6 , pp. 689-703
    • Capuzzo Dolcetta, I.1    Perthame, B.2
  • 15
    • 0003211244 scopus 로고
    • Convex, analysis and measurable multifunctions
    • Berlin: Springer
    • Castaing, C., Valadier, M.: Convex, analysis and measurable multifunctions. Lect. Notes Math. 580. Berlin: Springer 1977
    • (1977) Lect. Notes Math. , vol.580
    • Castaing, C.1    Valadier, M.2
  • 16
    • 0040071029 scopus 로고
    • On uniqueness almost everywhere for monotonic differential inclusions
    • Cellina, A.: On uniqueness almost everywhere for monotonic differential inclusions. Nonlinear Anal., Theory Methods Appl. 25, 899-903 (1995)
    • (1995) Nonlinear Anal., Theory Methods Appl. , vol.25 , pp. 899-903
    • Cellina, A.1
  • 18
    • 0036487117 scopus 로고    scopus 로고
    • Uniqueness of continuous solutions for BV vector fields
    • Colombini, F., Lerner, N.: Uniqueness of continuous solutions for BV vector fields. Duke Math. J. 111, 357-384 (2002)
    • (2002) Duke Math. J. , vol.111 , pp. 357-384
    • Colombini, F.1    Lerner, N.2
  • 21
    • 0035585521 scopus 로고    scopus 로고
    • A variational approach for the 2-dimensional semi-geostrophic shallow water equations
    • Cullen, M., Gangbo, W.: A variational approach for the 2-dimensional semi-geostrophic shallow water equations. Arch. Ration. Mech. Anal. 156, 241-273 (2001)
    • (2001) Arch. Ration. Mech. Anal. , vol.156 , pp. 241-273
    • Cullen, M.1    Gangbo, W.2
  • 23
    • 0142033336 scopus 로고    scopus 로고
    • Structure of entropy solutions to the eikonal equation
    • De Lellis, C., Otto, F.: Structure of entropy solutions to the eikonal equation. J. Eur. Math. Soc. (JEMS) 5, 107-145 (2003)
    • (2003) J. Eur. Math. Soc. (JEMS) , vol.5 , pp. 107-145
    • De Lellis, C.1    Otto, F.2
  • 24
    • 0242627517 scopus 로고    scopus 로고
    • Structure of entropy solutions for multi-dimensional conservation laws
    • De Lellis, C., Otto, F., Westdickenberg, M.: Structure of entropy solutions for multi-dimensional conservation laws. Arch. Ration. Mech. Anal. 170, 137-184 (2003)
    • (2003) Arch. Ration. Mech. Anal. , vol.170 , pp. 137-184
    • De Lellis, C.1    Otto, F.2    Westdickenberg, M.3
  • 25
    • 0141738641 scopus 로고    scopus 로고
    • Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d'un hyperplan
    • De Pauw, N.: Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d'un hyperplan. C.R. Math. Sci. Acad. Paris 337, 249-252 (2003)
    • (2003) C.R. Math. Sci. Acad. Paris , vol.337 , pp. 249-252
    • De Pauw, N.1
  • 26
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • Di Perna, R.J., Lions, P.L.: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511-547 (1989)
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • Di Perna, R.J.1    Lions, P.L.2
  • 31
    • 0032043481 scopus 로고    scopus 로고
    • Sur les équations différentielles ordinaires et les équations de transport
    • Lions, P.L.: Sur les équations différentielles ordinaires et les équations de transport. C. R. Acad. Sci., Paris, Sér. I, Math. 326, 833-838 (1998)
    • (1998) C. R. Acad. Sci., Paris, Sér. I, Math. , vol.326 , pp. 833-838
    • Lions, P.L.1
  • 32
    • 0033474746 scopus 로고    scopus 로고
    • Linear transport equation with discontinuous coefficients
    • Petrova, G., Popov, B.: Linear transport equation with discontinuous coefficients. Commun. Partial Differ. Equations 24, 1849-1873 (1999)
    • (1999) Commun. Partial Differ. Equations , vol.24 , pp. 1849-1873
    • Petrova, G.1    Popov, B.2
  • 33
    • 0000389658 scopus 로고    scopus 로고
    • Measure solutions to the liner multidimensional transport equation with non-smooth coefficients
    • Poupaud, F., Rascle, M.: Measure solutions to the liner multidimensional transport equation with non-smooth coefficients. Commun. Partial Differ. Equations 22, 337-358 (1997)
    • (1997) Commun. Partial Differ. Equations , vol.22 , pp. 337-358
    • Poupaud, F.1    Rascle, M.2


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