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

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.
44
3
2179
2203
http://preprints.sissa.it/xmlui/handle/1963/4168
Bianchini, S.; Tonon, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/14066
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