Homogenization of reflected semilinear PDE with nonlinear Neumann boundary condition

TL;DR

This paper investigates the homogenization of semi-linear reflected PDEs with nonlinear Neumann boundary conditions using probabilistic methods and weak convergence of reflected GBSDEs.

Contribution

It introduces a probabilistic approach to homogenize reflected PDEs with nonlinear boundary conditions, expanding the theoretical framework.

Findings

Established homogenization results for reflected PDEs with nonlinear Neumann conditions

Developed a probabilistic proof using reflected GBSDEs

Extended the theory of homogenization to a new class of PDEs

Abstract

We study the homogenization problem of semi linear reflected partial differential equations (reflected PDEs for short) with nonlinear Neumann conditions. The non-linear term is a function of the solution but not of its gradient. The proof are fully probabilistic and uses weak convergence of associated reflected generalized backward differential stochastic equations (reflected GBSDEs in short).