Boundary regularity via Uhlenbeck-Rivi\`ere decomposition
Analysis of PDEs
2013-01-23 v2
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.
Cite
@article{arxiv.0807.4455,
title = {Boundary regularity via Uhlenbeck-Rivi\`ere decomposition},
author = {Frank Müller and Armin Schikorra},
journal= {arXiv preprint arXiv:0807.4455},
year = {2013}
}
Comments
20 pages