Stochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environment
Wenjia Jing, Panagiotis E. Souganidis, Hung V. Tran · Research in the Mathematical Sciences · 2017
We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient), we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends previous work that required uniform ellipticity and space-time homogeneity for the diffusion.