Calculus of Variations and Geometric Measure Theory

M. Bardi - A. Cesaroni - E. Topp

Cauchy problem and periodic homogenization for nonlocal Hamilton-Jacobi equations with coercive gradient terms

created by cesaroni on 16 Jun 2018
modified by bardi on 23 Sep 2021


Published Paper

Inserted: 16 jun 2018
Last Updated: 23 sep 2021

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 150
Number: 6
Pages: 3028 - 3059
Year: 2020
Doi: 10.1017/prm.2019.56

ArXiv: 1806.05930 PDF


This paper deals with the periodic homogenization of nonlocal parabolic Hamilton-Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integro-differential equations that can be of independent interest.

Keywords: Homogenization, Viscosity solutions, Hamilton-Jacobi equations, Comparison principle, integro-differential equations, fractional Laplacians