Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition

We study the behaviour at boundary points of a solution of the Dirichlet problem with continuous boundary function for the Euler equation generated by the Lagrangian |∇u|p(x)/p(x) with variable p=p(x) that has logarithmic modulus of continuity and satisfies the condition 1<p1≤p(x)≤p2<∞. We obtain a regularity criterion for a boundary point of Wiener type, an estimate for the modulus of continuity of the solution near a regular boundary point, and geometric conditions for regularity