We consider the limit of sequences of normalized (s, 2)-Gagliardo seminorms with an oscillating coefficient as s→ 1 . In a seminal paper by Bourgain et al. (Another look at Sobolev spaces. In: Optimal control and partial differential equations. IOS, Amsterdam, pp 439–455, 2001) it is proven that if the coefficient is constant then this sequence Γ -converges to a multiple of the Dirichlet integral. Here we prove that, if we denote by ε the scale of the oscillations and we assume that 1-s<[removed]
