The two-scale-transformation method

We present the two-scale-transformation method which allows rigorous homogenisation of problems defined in locally periodic domains. This transforms such into domains order to facilitate passage limit. The idea transforming originates from evolving microstructure and has been applied several works. However, only substitute was proven, whereas itself just postulated (i.e. equivalence actual problem had be assumed). In this work, we develop further formulate a two-scale convergence concept for microscopic transformation. Thus, can prove that is equivalent problem. Moreover, show new transformation rule gradients enables derivation limit are now transformationally independent.