Correctors in Linear Homogenization

Abstract

I understood the necessity of defining correctors from a remark of Ivo BABUšKA, when I first met him in May 1975, at a conference that he organized at UMD, College Park, MD. He told me that in elasticity,1 it is not the average stress which is important but the maximum stress, since plastic behaviour or cracks may start at some points, where the boundary of the elastic domain is reached, while the average stress is still much below the critical level where non–elastic behaviour occurs.² One then needs to study amplifying factors, for computing local stresses from an average stress.