Alfonso Sorrentino (University of Rome Tor Vergata)
Abstract: In this talk, I will present a stochastic homogenization result for first-order Hamilton-Jacobi equations on Riemannian manifolds within a stationary ergodic random environment. The setting involves a finitely generated abelian group of isometries acting freely and cocompactly on the manifold, together with a family of Hamiltonians parametrized by an ergodic probability space. Under standard assumptions – including strict convexity and superlinear coercivity in the momentum variable -I will show that as the scaling parameter tends to zero, the viscosity solutions to the rescaled Hamilton-Jacobi equation converge almost surely and locally uniformly to the solution of a deterministic homogenized equation posed on a Euclidean space of dimension d, where d corresponds to the rank of the acting group. This is based on joint work with Marco Pozza.