Homogenization and Vanishing Viscosity in Fully Nonlinear Elliptic Equations: Rate of Convergence Estimates
Fabio Camilli, Annalisa Cesaroni, Claudio Marchi · Advanced Nonlinear Studies · 2011
Abstract This paper is devoted to studying the behavior as ε → 0 of the equations u ε + H(x, x/ε, Du ε , ε γ D 2 u ε ) = 0 with γ > 0. It is known that, under some periodicity and ellipticity or coercivity assumptions, the solution u ε converges to the solution u of an effective equation u + H̅(x, Du) = 0, with an effective Hamiltonian H̅ dependent on the value of γ. The main purpose of this paper is to estimate the rate of convergence of u ε to u. Moreover we discuss some examples and model problems.