SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)
Résumé
In this paper we prove the SBV regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation under the hypothesis of uniform convexity of the Hamiltonian H(t,x,D_xu) in the last variable. This result extends the result of Bianchini, De Lellis and Robyr obtained for a Hamiltonian H(D_x u) which depends only on the spatial gradient of the solution.
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