In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation partial derivative(t)u + H(t, x, D(x)u) = 0 in Omega subset of [0, T] x R-n 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(D(x)u) which depends only on the spatial gradient of the solution.
SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) / Bianchini, S.; Tonon, D.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 44:3(2012), pp. 2179-2203. [10.1137/110827272]
SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)
Bianchini, S.;Tonon, D.
2012-01-01
Abstract
In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation partial derivative(t)u + H(t, x, D(x)u) = 0 in Omega subset of [0, T] x R-n 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(D(x)u) which depends only on the spatial gradient of the solution.| File | Dimensione | Formato | |
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