Periodic Homogenization for Weakly Elliptic Hamilton-Jacobi-Bellman\n Equations with Critical Fractional Diffusion

2020/02/21 by Adina Ciomaga, Ciomaga, Adina, Daria Ghilli +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2002.09252

openalex publication_date 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we establish periodic homogenization for\nHamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of\nintegro-differential type. We consider the case when the fractional diffusion\nhas the same order as the drift term, and is weakly elliptic. The outcome of\nthe paper is twofold. One one hand, we provide Lipschitz regularity results for\nweakly elliptic non-local HJB, extending the results previously obtained in\n[8]. On the other hand, we establish a convergence result, based on half\nrelaxed limits and a comparison principle for the effective problem. The latter\nstrongly relies on the regularity and the ellipticity properties of the\neffective Hamiltonian, for which a fine Lipschitz estimate of the corrector\nplays a crucial role.\n

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