Homogenization of semi-linear PDEs with discontinuous coefficients

We study the asymptotic behavior of the solution of semi-linear PDEs. Neither periodicity nor ergodicity assumptions are assumed. The coefficients admit only a limit in a C̀esaro sense. In such a case, the limit coefficients may have discontinuity. We use probabilistic approach based on weak convergence techniques for the associated backward stochastic differential equation in the S-topology. We establish weak continuity for the flow of the limit diffusion process and related the PDE limit to the backward stochastic differential equation via the representation of L-viscosity solution. Keys words: Backward stochastic differential equations (BSDEs), L-viscosity solution for PDEs, homogenization, S-topology, limit in C̀esaro sense. MSC 2000 subject classifications, 60H20, 60H30, 35K60.