Application of Newton’s method to a homogenization problem
The homogenization of a family (Pε) of uniformly elliptic semilinear partial differential equations of second order is studied. The main result is that any non-singular solutionu of the homogenized problem (P) is the limit of non-singular solutions of (Pε). The method consists of specifying a functionwε starting from which the Newton iterates converge to a solutionuε ofPε. These solutionsuε converge to the given solutionu of (P).