  We prove that weak solutions of systems with skew-symmetric structure, which
possess a continuous boundary trace, have to be continuous up to the boundary.
This applies, e.g., to the H-surface system with bounded H and thus extends an
earlier result by P. Strzelecki and proves the natural counterpart of a
conjecture by E. Heinz. Methodically, we use estimates below natural exponents
of integrability and a recent decomposition result by T.Rivi\`ere.
