A General Technique to Prove Upper Bounds for Singular Perturbation Problems

* Firstly, we wish to find a lower bound, i.e. the functional I(φ) such that for every family {φε}ε>0, satisfying φε → φ as ε → 0 , we have limε→0+ Iε(φε) ≥ I(φ). ** Secondly, we wish to find an upper bound, i.e. the functional I(φ) such that there exists the family {ψε}ε>0, satisfying ψε → φ as ε → 0 , and we have limε→0+ Iε(ψε) ≤ I(φ). *** If we obtain I(φ) = I(φ) := I(φ), then I(φ) will be the Γ-limit of Iε(φ).