Boundary regularity via Uhlenbeck-Rivière decomposition

Frank Müller, Armin Schikorra

Published 2008-07-28, updated 2008-08-12Version 2

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.