ASYMPTOTIC BEHAVIOUR OF THE ENERGY INTEGRAL OF A TWO-PARAMETER HOMOGENIZATION PROBLEM WITH NONLINEAR PERIODIC ROBIN BOUNDARY CONDITIONS

We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter delta. The relative size of each periodic perforation is determined by a positive parameter epsilon. Under suitable assumptions, such a problem admits a family of solutions which depends on epsilon and delta. We analyse the behaviour the energy integral of such a family as (epsilon, delta) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.