Some Homogenization and Corrector Results for Nonlinear Monotone Operators
Peter Wall · Journal of Nonlinear Mathematical Physics · 1998
This paper deals with the limit behaviour of the solutions of quasi-linear equations of the formdiv (a (x, x/ε h , Du h )) = f h on Ω with Dirichlet boundary conditions.The sequence (ε h ) tends to 0 and the map a(x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions.It is proved that u h → u weakly in H 1,2 0 (Ω), where u is the solution of a homogenized problemdiv(b(x, Du)) = f on Ω.We also prove some corrector results, i.e. we find (P h ) such that Du h -