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

Abstract

This paper is devoted to studying the behavior as ε ← 0 of the equations uε + H(x,x/ε, Duε, εγD2uε) = 0 with γ ≥ 0. It is known that, under some periodicity and ellipticity or coercivity assumptions, the solution uε converges to the solution u of an effective equation u + H(x, Du) = 0, with an effective Hamiltonian H dependent on the value of γ. The main purpose of this paper is to estimate the rate of convergence of uε to u. Moreover we discuss some examples and model problems.