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

• Main Authors: Mohamed Marzougue, Ibrahima Sane
• Format: Article
• Language: English
• Published: Elsevier 2021-06-01
• Series: Partial Differential Equations in Applied Mathematics
• Subjects: Homogenization; Elliptic degenerate PDEs; Neumann-boundary condition; Stochastic differential equation; Backward stochastic differential equation
• Online Access: http://www.sciencedirect.com/science/article/pii/S2666818121000012

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.