Hölder continuity of p(x)-superharmonic functions

In this paper we show that a solution of the equation −Δp(x)u=μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤Crn−p(x)+α(p(x)−1) for any ball Br(x)⊂Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpeläinen and Zhong for the p-Laplace operator with p constant.