Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem

2013/01/17 by Claudio Marchi, Marchi, Claudio
Computer Science · Engineering · Mathematics · #35B27 #35B30 #35J60 #49L25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP #msc:35B27 #msc:35B30 #msc:35J60 #msc:49L25

paper · pdf · doi:10.48550/arxiv.1301.4105

openalex publication_date 2013/01/17 · arxiv created 2013/06/14 · arxiv updated 2013/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to establish continuous dependence estimates for the ergodic problem for Bellman operators (namely, estimates of (v₁-v₂) where v₁ and v₂ solve two equations with different coefficients). We shall obtain an estimate of ||v₁-v₂||_∞ with an explicit dependence on the L^∞-distance between the coefficients and an explicit characterization of the constants and also, under some regularity conditions, an estimate of ||v₁-v₂||_C²(\Rⁿ). Afterwards, the former result will be crucial in the estimate of the rate of convergence for the homogenization of Bellman equations. In some regular cases, we shall obtain the same rate of convergence established in the monographs [11,26] for regular linear problems.

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