Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws

Archive for Rational Mechanics and Analysis

Volumn 170, Issue 2, 2003, Pages 137-184

  De Lellis, Camillo ^a   Otto, Felix ^b   Westdickenberg, Michael ^b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242627517     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-003-0270-9     Document Type: Article

References (27)

1. AMBROSIO, L., FUSCO, N., PALLARA, D.: Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, Clarendon Press, Oxford, 2000
2. AMBROSIO, L., KIRCHHEIM, B., LECUMBERRY, M., RIVIÈRE, T.: The local structure of Néel Walls. Nonlinear Problems in Mathematical Physics and Related Topics II. In Honour of Professor O.A. Ladyzhenskaya. International Mathematical Series vol. 2. Kluwer Academic, 2002
3. AMBROSIO, L., LECUMBERRY, M., RIVIÈRE, T.: Viscosity property of minimizing micromagnetic configurations. Comm. Pure Appl. Math. 56, 681-688 (2003)
4. BÉNILAN, P., CRANDALL, M.: Regularizing effect of homogeneous evolution equations. Contributions to analysis and geometry (Baltimore, Md., 1980), Johns Hopkins Univ. Press, 1981, pp. 23-39
5. p. Math. Scand. 19, 27-37 (1966)
6. BRESSAN, A.: Hyperbolic systems of conservation laws. The one dimensional Cauchy problem. Oxford Lecture Series in Mathematics and its Applications vol. 20. Oxford University Press, Oxford, 2000
7. CHEN, G.-Q., FRID, H.: Divergence-measure fields and hyperbolic conservation laws. Arch. Rational Mech. Anal. 147, 89-118 (1999)
8. CHEN, G.-Q., RASCLE, M.: Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws. Arch. Rational Mech. Anal. 153, 205-220 (2000)
9. CHEVERRY, C.: Regularizing effects for multidimensional scalar conservation laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 17, 413-472 (2000)
10. DAFERMOS, C.: Hyperbolic conservation laws in continuum physics. Grundlehren der Mathematischen Wissenschaften vol. 325. Springer-Verlag, Berlin, 2000
11. DE LELLIS, C., OTTO, F.: Structure of entropy solutions to the eikonal equation. J. Eur. Math. Soc. 5, 107-145 (2003)
12. P regularity of velocity averages. Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 271-287 (1991)
13. EVANS, L.C., GARIEPY, R.F.: Measure theory and fine properties of functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992
14. GOLSE, S., LIONS, P.-L., PERTHAME, B., SENTIS, R.: Regularity of the moments of the solution of a transport equation. J. Fund. Anal. 76, 110-125 (1988)
15. JABIN, P.-E., OTTO, F., PERTHAME, B.: Line-energy Ginzburg-Landau models: zero-energy states. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 1, 187-202 (2002)
16. JABIN, P.-E., PERTHAME, B.: Regularity in kinetic formulations via averaging lemmas: A tribute to J.-L. Lions. ESAIM Control Optim. Calc. Var. 8, 761-774 (2002)
17. KRUZKOV, S.N.: First order quasilinear equations in several independent variables. Math USSR-Sbornik 10, 217-243 (1970)
18. LECUMBERRY, M., RIVIÈRE, T.: The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1 + 1 D. Preprint 44 in HTTP://WWW.MATH.ETHZ.CH/RIVIERE/PUB.HTML.
19. LIONS, P.-L., PERTHAME, B., TADMOR, E.: A kinetic formulation of multidimensional scalar conservation laws and related questions. J. AMS 7, 169-191 (1994)
20. MATTILA, P.: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability. Cambridge Studies in Advanced Mathematics vol. 44. Cambridge University Press, Cambridge, 1995
21. OLEINIK, O.A.: Discontinuous solutions of nonlinear differential equations. Transl. AMS Set 2 26, 95-172 (1957)
22. OTTO, F.: A regularizing effect of nonlinear transport equations. Quart. Appl. Math. 56, 355-375 (1998)
23. RUDIN, W.: Functional Analysis. International Series in Pure and Applied Math., McGraw-Hill, second edition, 1991
24. SERRE, D.: Systems of conservation laws. 1. Hyperbolicity, entropies, shock waves. Cambridge University Press, Cambridge, 2000
25. TARTAR, L.: Compensated compactness and applications to partial differential equations. Nonlinear analysis and mechanics: Herriot-Watt Symposium, Vol IV, Res. Notes in Math. 39, 1979, pp. 136-212
26. VASSEUR, A.: Strong traces for solutions of multidimensional scalar conservation laws. Arch. Rational Mech. Anal. 160, 181-193 (2001)
27. WESTDICKENBERG, M.: Some new velocity averaging results. SIAM J. Math. Anal. 33, 1007-1032 (2002)