Hyperbolic equations and SBV functions
- [1] Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Journées Équations aux dérivées partielles (2010)
- page 1-10
- ISSN: 0752-0360
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topDe Lellis, Camillo. "Hyperbolic equations and SBV functions." Journées Équations aux dérivées partielles (2010): 1-10. <http://eudml.org/doc/116387>.
@article{DeLellis2010,
abstract = {In this article we survey some recent results in the regularity theory of admissible solutions to hyperbolic conservation laws and Hamilton-Jacobi equations.},
affiliation = {Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland},
author = {De Lellis, Camillo},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-10},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Hyperbolic equations and SBV functions},
url = {http://eudml.org/doc/116387},
year = {2010},
}
TY - JOUR
AU - De Lellis, Camillo
TI - Hyperbolic equations and SBV functions
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 10
AB - In this article we survey some recent results in the regularity theory of admissible solutions to hyperbolic conservation laws and Hamilton-Jacobi equations.
LA - eng
UR - http://eudml.org/doc/116387
ER -
References
top- Alberti, G., and Ambrosio, L. A geometrical approach to monotone functions in . Math. Z. 230, 2 (1999), 259–316. Zbl0934.49025MR1676726
- Ambrosio, L., and De Lellis, C. A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. J. Hyperbolic Differ. Equ. 1, 4 (2004), 813–826. Zbl1071.35032MR2111584
- Ambrosio, L., De Lellis, C., and Malý, J. On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems. In Perspectives in nonlinear partial differential equations, vol. 446 of Contemp. Math. Amer. Math. Soc., Providence, RI, 2007, pp. 31–67. Zbl1200.49043MR2373724
- Ambrosio, L., Fusco, N., and Pallara, D.Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, 2000. Zbl0957.49001MR1857292
- Ancona, F., and Coclite, G. M. On the attainable set for Temple class systems with boundary controls. SIAM J. Control Optim. 43, 6 (2005), 2166–2190 (electronic). Zbl1087.93010MR2179483
- Ancona, F., and Marson, A. On the attainable set for scalar nonlinear conservation laws with boundary control. SIAM J. Control Optim. 36, 1 (1998), 290–312 (electronic). Zbl0919.35082MR1616586
- Ancona, F., and Marson, A. Asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point. In Control methods in PDE-dynamical systems, vol. 426 of Contemp. Math. Amer. Math. Soc., Providence, RI, 2007, pp. 1–43. Zbl1128.35069MR2311519
- Ancona, F., and Nguyen, K. T. SBV regularity for solutions to genuinely nonlinear Temple systems of balance laws. In preparation.
- Bianchini, S., and Caravenna, L. SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws. In preparation. Zbl1261.35089
- Bianchini, S., De Lellis, C., and Robyr, R. SBV regularity for Hamilton-Jacobi equations in . To appear in Arch. Rat. Mech. Anal. (2010). Zbl1223.49039
- Bressan, A.Hyperbolic systems of conservation laws, vol. 20 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. Zbl0997.35002MR1816648
- Bressan, A., and Marson, A. A maximum principle for optimally controlled systems of conservation laws. Rend. Sem. Mat. Univ. Padova 94 (1995), 79–94. Zbl0935.49012
- Bressan, A., and Shen, W. Optimality conditions for solutions to hyperbolic balance laws. In Control methods in PDE-dynamical systems, vol. 426 of Contemp. Math. Amer. Math. Soc., Providence, RI, 2007, pp. 129–152. Zbl05194890MR2311524
- Cannarsa, P., and Sinestrari, C.Semiconcave functions, Hamilton-Jacobi equations, and optimal control. Progress in Nonlinear Differential Equations and their Applications, 58. Birkhäuser Boston Inc., Boston, MA, 2004. Zbl1095.49003MR2041617
- Dafermos, C. M.Hyperbolic conservation laws in continuum physics, vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 2000. Zbl0940.35002MR1763936
- Dafermos, C. M. Wave fans are special. Acta Math. Appl. Sin. Engl. Ser. 24, 3 (2008), 369–374. Zbl1170.35478MR2433867
- De Giorgi, E., and Ambrosio, L. New functionals in the calculus of variations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 82, 2 (1988), 199–210 (1989). Zbl0715.49014MR1152641
- Evans, L. C.Partial differential equations, vol. 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998. Zbl0902.35002MR1625845
- Robyr, R. SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function. J. Hyperbolic Differ. Equ. 5, 2 (2008), 449–475. Zbl1152.35074MR2420006
- Tonon, D.Personal communication..
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