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.

Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case / Davini, Andrea; Siconolfi, Antonio. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 345:4(2009), pp. 749-782. [10.1007/s00208-009-0372-2]

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

DAVINI, ANDREA;SICONOLFI, Antonio
2009

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.
2009
01 Pubblicazione su rivista::01a Articolo in rivista
Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case / Davini, Andrea; Siconolfi, Antonio. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 345:4(2009), pp. 749-782. [10.1007/s00208-009-0372-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/228820
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