In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation ∂tu + H(t, x,Dxu) = 0 in φ ∪ [0, T] × Rn under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis, and Robyr obtained for a Hamiltonian H = H(Dxu) which depends only on the spatial gradient of the solution.
SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t, x)
Tonon D.
2012
Abstract
In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation ∂tu + H(t, x,Dxu) = 0 in φ ∪ [0, T] × Rn under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis, and Robyr obtained for a Hamiltonian H = H(Dxu) which depends only on the spatial gradient of the solution.
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