SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian

Stefano Bianchini 1 Daniela Tonon 2
2 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : In this paper we consider a viscosity solution u of the Hamilton-Jacobi equation where H is smooth and convex. We prove that when d(t,⋅):=Hp(Dxu(t,⋅)), Hp:=∇H is BV for all t∈[0,T] and suitable hypotheses on the Lagrangian L hold, the Radon measure can have Cantor part only for a countable number of tʼs in [0,T]. This result extends a result of Robyr for genuinely nonlinear scalar balance laws and a result of Bianchini, De Lellis and Robyr for uniformly convex Hamiltonians.
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Journal of Mathematical Analysis and applications, Elsevier, 2012, 391 (1), pp.190-208. 〈10.1016/j.jmaa.2012.02.017〉
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https://hal.inria.fr/hal-00724838
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 18:07:58
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Stefano Bianchini, Daniela Tonon. SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian. Journal of Mathematical Analysis and applications, Elsevier, 2012, 391 (1), pp.190-208. 〈10.1016/j.jmaa.2012.02.017〉. 〈hal-00724838〉

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