Homogenization and vanishing viscosity in fully nonlinear elliptic equations: rate of convergence estimates.

This paper is devoted to studying the behavior as epsilon -> 0 of the equations u(epsilon) + H(x, x/epsilon, Du(epsilon), epsilon(gamma)D(2)u(epsilon)) = 0 with gamma > 0. It is known that, under some periodicity and ellipticity or coercivity assumptions, the solution u(c) converges to the solution u of an effective equation u + (H) over bar( x, Du) = 0, with an effective Hamiltonian (H) over bar dependent on the value of gamma. The main purpose of this paper is to estimate the rate of convergence of u(epsilon) to u. Moreover we discuss some examples and model problems.