  We consider an energy functional on surface immersions which includes
contributions from both boundary and interior. Inspired by physical examples,
the boundary is modeled as the center line of a generalized Kirchhoff elastic
rod, while the interior term is arbitrarily dependent on the mean curvature and
linearly dependent on the Gaussian curvature. We study equilibrium
configurations for this energy in general among topological disks, as well as
specifically for the class of examples known as p-Willmore energies.
