  In this paper we consider the problem of prescribing the Gaussian and
geodesic curvature on a disk and its boundary, respectively, via a conformal
change of the metric. This leads us to a Liouville-type equation with a
nonlinear Neumann boundary condition. We address the question of existence by
setting the problem in a variational framework which seems to be completely new
in the literature. We are able to find minimizers under symmetry assumptions.
