Local Hölder regularity of the gradients for the elliptic p(x)p(x)-Laplacian equation

In this paper we obtain the interior Hölder regularity of the gradients of weak solutions for the elliptic p(x)p(x)-Laplacian equation div((A∇u⋅∇u)p(x)−22A∇u)=div(|f|p(x)−2f), under some proper assumptions on the Hölder continuous functions p,f and AA.