We study the equation $u_t+ H(x, Du) = 0 in $\R^N\yimes [0,T]$ with Hamiltonian $H(x, p)$ measurable with respect to the state variable, and convex and coercive in $p$. We introduce a notion of solution based on viscosity test functions, appropriate averages in measure-theoretic sense of the Hamiltonian, and $t$-partial-sup-convolutions. We get existence results, comparison principles, and stability properties. We show that our solutions are uniform limits of viscosity solutions (in the sense of Crandall and Lions) of approximated continuous equations.

Time-dependent measurable Hamilton-Jacobi equations / Camilli, Fabio; Siconolfi, Antonio. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 30:(2005), pp. 813-847. [10.1081/PDE-200059292]

Time-dependent measurable Hamilton-Jacobi equations

CAMILLI, FABIO;SICONOLFI, Antonio
2005

Abstract

We study the equation $u_t+ H(x, Du) = 0 in $\R^N\yimes [0,T]$ with Hamiltonian $H(x, p)$ measurable with respect to the state variable, and convex and coercive in $p$. We introduce a notion of solution based on viscosity test functions, appropriate averages in measure-theoretic sense of the Hamiltonian, and $t$-partial-sup-convolutions. We get existence results, comparison principles, and stability properties. We show that our solutions are uniform limits of viscosity solutions (in the sense of Crandall and Lions) of approximated continuous equations.
2005
HAMILTON-JACOBI EQUATIONS; Measurable Hamiltonian
01 Pubblicazione su rivista::01a Articolo in rivista
Time-dependent measurable Hamilton-Jacobi equations / Camilli, Fabio; Siconolfi, Antonio. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 30:(2005), pp. 813-847. [10.1081/PDE-200059292]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/240533
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