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arXiv · 0807.4455

Boundary regularity via Uhlenbeck-Rivi\`ere decomposition

Frank Müller·Armin Schikorra
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Abstract

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.

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Frank Müller, Armin Schikorra. 2008-07-28. Boundary regularity via Uhlenbeck-Rivi\`ere decomposition. https://doi.org/10.1524/anly.2009.1025

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