Boundary continuity of solutions to elliptic equations with nonstandard growth

We study regularity properties of weak solutions to elliptic equations involving variable growth exponents. We prove the sufficiency of a Wiener type criterion for the regularity of boundary points. This criterion is formulated in terms of the natural capacity involving the variable growth exponent. We also prove the Hölder continuity of weak solutions up to the boundary in domains with uniformly fat complements, provided that the boundary values are Hölder continuous.