Analytical and numerical periodic homogenization of Hamilton--Jacobi--Bellman and Isaacs equations in a $W^{2,p}$ Cordes framework
Year: 2026
Type: preprint
Abstract: We study periodic homogenization of fully-nonlinear second-order Hamilton--Jacobi--Bellman and Isaacs equations subject to a homogeneous Dirichlet boundary condition and the numerical approximation of the effective Hamiltonian, where the diffusion matrix is assumed to satisfy the Cordes condition. In the first part, assuming the Cordes parameter is sufficiently large, we show existence and uniqueness of $W^{2,p}$ solutions to the true cell problem, prove homogenization under minimal regularity assumptions, and establish a quantitative homogenization result. In the second part, we propose and rigorously analyze $W^{2,p}$-conforming and mixed finite element methods for the approximation of the corrector, which are then used in the approximation of the effective Hamiltonian. The key tool used throughout this work is Campanato's concept of near operators.
Source: arXiv (Cornell University)
Authors: Sprekeler, Timo, Tran, Hung V.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221771512