Special issue on the honor of Gerard CohenInternational audienceThe differential uniformity of a mapping F:F2n→F2n is defined as the maximum number of solutions x for equations F(x+a)+F(x)=b when a ̸ = 0 and b run over F2n. In this paper we study the question whether it is possible to determine the differential uniformity of a mapping by considering not all elements a ̸ = 0, but only those from a special proper subset of F2n0. We show that the answer is " yes " , when F has differential uniformity 2, that is if F is APN. In this case it is enough to take a ̸ = 0 on a hyperplane in F2n. Further we show that also for a large family of mappings F of a special shape, it is enough to consider a from a suitable multiplicative subgroup of F2n