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

Stefano Bianchini 1 Daniela Tonon 2
2 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
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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https://hal.inria.fr/hal-00724838
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Submitted on : Wednesday, August 22, 2012 - 6:07:58 PM
Last modification on : Saturday, June 19, 2021 - 3:50:27 AM

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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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