Relative influence of two small parameters in non uniformly elliptic homogenization problems
Jeannine Saint Jean Paulin, Wiktor Eckhaus · Mathematical Methods in the Applied Sciences · 1985
Abstract We study three elliptic problems depending on two small parameters (ϵ = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (ϵ, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ϵ and δ; the relevant parameter is δϵ−2.