On correctors for linear elliptic homogenization in the presence of local defects

We consider the corrector equation associated, in homogenization theory, to a linear second-order elliptic equation in divergence form , when the diffusion coefficient is a locally perturbed periodic coefficient. The question under study is the existence (and uniqueness) of the corrector, strictly sublinear at infinity, with gradient in L-r if the local perturbation is itself L-r, . This work follows up on previous works of ours, providing an alternative, more general and versatile approach, based on an a priori estimate, for this well-posedness result. Equations in non-divergence form such as are also considered, along with various extensions. The case of general advection-diffusion equations is postponed to a future work. An appendix contains a corrigendum to one of our earlier publication.