Title: Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations,
Abstract: We study the stochastic homogenization for a Cauchy problem for a first-order
Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient
variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$ where
$\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered
is consistent with the underlying Carnot group structure, thus anisotropic. We
will prove that under suitable assumptions for the Hamiltonian, the solutions
of the $\varepsilon$-problem converge to a deterministic function which can be
characterized as the unique (viscosity) solution of a suitable deterministic
Hamilton-Jacobi problem.