Hölder regularity for the gradients of solutions of the strong p(x)-Laplacian

Under some assumptions on the continuous function p(x)>1, we obtain the local C1,α regularity of solutions of the strong p(x)-Laplacian−div(|∇u|p(x)−2∇u)+|∇u|p(x)−2log(|∇u|)∇u⋅∇p=0 by using the integral estimates in Campanato spaces.