| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 43 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/cocv/2023038 | |
| Published online | 09 June 2023 | |
Rates of convergence in periodic homogenization of nonlocal Hamilton–Jacobi–Bellman equations*,, **
1
Departamento de Matemática, Universidad de Concepción, Avenida Esteban Iturra s/n, Barrio Universitario,
Casilla 160 C,
Concepción,
Chile
2
Departamento de Matemática y C.C., Universidad de Santiago de Chile, Casilla 307, Santiago, Chile, and Instituto de Matemáticas, Universidade Federal do Rio de Janeiro,
Rio de Janeiro,
RJ
21941-909,
Brazil
*** Corresponding author: erwin.topp@usach.cl
Received:
5
August
2022
Accepted:
5
May
2023
In this paper we provide a rate of convergence for periodic homogenization of Hamilton–Jacobi–Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest.
Mathematics Subject Classification: 35B27 / 35B40 / 35D40 / 35R09 / 45K05
Key words: Periodic homogenization / Hamilton–Jacobi equations / rates of convergence / nonlocal equations / representation formulas / viscosity solutions
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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