We consider the Cauchy problem u(t) + H(x, Du) = 0, (x, t) epsilon R-N x (0, infinity), u(x, 0) = u(0)(x), x epsilon R-N, where H is measurable in x, continuous, convex and positive homogeneous in p. We adapt the definition of viscosity solution to the measurable framework and we prove that the unique viscosity solution is given by a representation formula of Hopf-Lax type.

An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations / Camilli, Fabio. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 57:(2004), pp. 265-286. [10.1016/j.na.2004.02.013]

An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations

CAMILLI, FABIO
2004

Abstract

We consider the Cauchy problem u(t) + H(x, Du) = 0, (x, t) epsilon R-N x (0, infinity), u(x, 0) = u(0)(x), x epsilon R-N, where H is measurable in x, continuous, convex and positive homogeneous in p. We adapt the definition of viscosity solution to the measurable framework and we prove that the unique viscosity solution is given by a representation formula of Hopf-Lax type.
Measurable Hamilton–Jacobi equations, Viscosity solutions, Hopf–Lax formulas, Approximation
01 Pubblicazione su rivista::01a Articolo in rivista
An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations / Camilli, Fabio. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 57:(2004), pp. 265-286. [10.1016/j.na.2004.02.013]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/43884
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