Validation of marine geoid models by utilizing hydrodynamic model and shipborne GNSS profiles
AbstractAn essential role of the FAMOS international cooperation project is to obtain new marine gravity observations over the Baltic Sea for improving gravimetric geoid modelling. To achieve targe...
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 $H$-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.