Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition

Abstract

In this paper, a semi-linear elliptic partial differential equation (PDE) with non linear Neumann boundary condition and rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of Rd. Our fully probabilistic method is based on the connection between PDEs and backward stochastic differential equations (BSDEs) with random terminal time and the weak convergence of a class of diffusion processes.

Keywords

• Homogenization
• Elliptic degenerate PDEs
• Neumann-boundary condition
• Stochastic differential equation
• Backward stochastic differential equation