Boundary regularity via Uhlenbeck-Rivière decomposition. (English) Zbl 1181.35102
Summary: 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 \(\Delta u= 2H(u)\partial_{x^1}u\wedge \partial_{x^2}u\) 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.
MSC:
35J62 | Quasilinear elliptic equations |
35B65 | Smoothness and regularity of solutions to PDEs |
53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
35D30 | Weak solutions to PDEs |
Keywords:
boundary regularity; systems with skew-symmetric structure; \(H\)-surface system; nonlinear decompositionReferences:
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