me understand the below : In this article, we consider minimizers of the functional X f ax jDuj dx; where X Rn is open and bounded and u : X ! RN. We show that even though the coefficient a satisfies only that a 2 W1;q loc X \ L1X, it nonetheless follows that u is partially Holder continuous on the set of regular points of Da. We note that the integrability exponent q > 1 is arbitrary, and so, the coefficient map x 7! ax can be very irregular. As an application we show that weak solutions of the elliptic system r a x f 0 a x jDuj Du jDuj 0; x 2 X satisfies the same partial Holder continuity. The model case we have in mind is r a x jDuj p2 Du 0: Finally, we also demonstrate that Du is also almost everywhere Holder continuo