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Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case

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Abstract

We perform a qualitative investigation of critical Hamilton–Jacobi equations, with stationary ergodic Hamiltonian, in dimension 1. We show the existence of approximate correctors, give characterizing conditions for the existence of correctors, provide Lax-type representation formulae and establish comparison principles. The results are applied to look into the corresponding effective Hamiltonian and to study a homogenization problem. In the analysis a crucial role is played by tools from stochastic geometry such as, for instance, closed random stationary sets.

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  1. Dip. di Matematica, “Sapienza” Università di Roma, P.le Aldo Moro 2, 00185, Rome, Italy

    Andrea Davini & Antonio Siconolfi

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  1. Andrea Davini
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  2. Antonio Siconolfi
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Correspondence to Antonio Siconolfi.

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Davini, A., Siconolfi, A. Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case. Math. Ann. 345, 749–782 (2009). https://doi.org/10.1007/s00208-009-0372-2

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  • DOI: https://doi.org/10.1007/s00208-009-0372-2

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