Abstract: Let us consider the following elliptic systems of second order
-D_α(A_i^α(x, u, Du))=B_i(x, u, Du), i=1, …, N, x∈Ω⊂Rⁿ, n ≥ 3 (1) and suppose
ⅰ)|A_i^α(x, u, Du)| ≤ L(1+|Du|);
ⅱ) (1+|p|)^-1 A_i^α(x, u, p)are Hölder-continuous functions with some exponent δ on Ω×R^N uniformly with respect to p, i.e.