Boundary regularity via Uhlenbeck–Rivière decomposition

By Frank Müller, Armin Schikorra. 2008

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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 Δu = 2H(u)∂x1u∧∂x2u 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. Rivière.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/6560115b7e522eecd19cf8b644a173c08f300c9b