  We analyze minimizers of the Lawrence-Doniach energy for three-dimensional
highly anisotropic superconductors with layered structure. For such a
superconductor occupying a bounded generalized cylinder in $\mathbb{R}^3$ with
equally spaced parallel layers, we assume an applied magnetic field that is
perpendicular to the layers with intensity $h_{ex}\sim|\ln\epsilon|$ as
$\epsilon\rightarrow 0$, where $\epsilon$ is the reciprocal of the
Ginzburg-Landau parameter. We prove compactness results for various physical
quantities of energy minimizers, and derive a Gamma-limit of the
Lawrence-Doniach energy as $\epsilon$ and the interlayer distance $s$ tend to
zero, under the additional assumption that the layers are weakly coupled (i.e.,
$s\gg\epsilon$).
