Stochastic homogenization of viscous Hamilton–Jacobi equations and applications
Scott Armstrong, Hung V. Tran · Analysis & PDE · 2014
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument that is based only on the subadditive structure of maximal subsolutions (i.e., solutions of the "metric problem").This permits us to give qualitative homogenization results under very general hypotheses: in particular, we treat nonuniformly coercive Hamiltonians that satisfy instead a weaker averaging condition.As an application, we derive a general quenched large deviation principle for diffusions in random environments and with absorbing random potentials.