Boundary regularity for conformally invariant variational problems with Neumann data
Abstract
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, enter perpendicularly into a support manifold. For example, harmonic maps, or -surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Riviere, that these maps satisfy a system with an antisymmetric potential, from which one can derive regularity of the solution. We show that these maps satisfy along the boundary a system with a nonlocal antisymmetric boundary potential which contains information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.
Cite
@article{arxiv.1703.10783,
title = {Boundary regularity for conformally invariant variational problems with Neumann data},
author = {Armin Schikorra},
journal= {arXiv preprint arXiv:1703.10783},
year = {2018}
}