Stochastic homogenization of quasilinear Hamilton–Jacobi equations and geometric motions

Abstract

We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvaturemotion and others describing geometric motions of level sets as well as alarge class of viscous, non-convex Hamilton-Jacobi equations. The mainresults include the first proof of qualitative stochastic homogenization forsuch equations. We also present quantitative error estimates which give analgebraic rate of homogenization.