Global weighted estimates for quasilinear elliptic equations with non-standard growth

In this paper we obtain a new global gradient estimates in weighted Lorentz spaces for weak solutions of p(x)p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, the maximal function technique and the appropriate localization method are the main analytical tools. Our results improve the known results for such equations.