In this paper we consider a viscosity solution u of the Hamilton-Jacobi equation partial derivative(t)u + H(D(x)u) = 0 in Omega subset of [0,T] x R-n. where H is smooth and convex. We prove that when d(t,center dot) := H-p(D(x)u(t,center dot)), H-p := del H is BV for all t epsilon [0, T] and suitable hypotheses on the Lagrangian L hold, the Radon measure divd(t,center dot) can have Cantor part only for a countable number of t's 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.
SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian / Bianchini, S.; Tonon, D.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 391:1(2012), pp. 190-208. [10.1016/j.jmaa.2012.02.017]
SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian
Bianchini, S.;Tonon, D.
2012-01-01
Abstract
In this paper we consider a viscosity solution u of the Hamilton-Jacobi equation partial derivative(t)u + H(D(x)u) = 0 in Omega subset of [0,T] x R-n. where H is smooth and convex. We prove that when d(t,center dot) := H-p(D(x)u(t,center dot)), H-p := del H is BV for all t epsilon [0, T] and suitable hypotheses on the Lagrangian L hold, the Radon measure divd(t,center dot) can have Cantor part only for a countable number of t's 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.File | Dimensione | Formato | |
---|---|---|---|
sbv.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Non specificato
Dimensione
413.74 kB
Formato
Adobe PDF
|
413.74 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.