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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.