  We consider a one-dimensional variational problem arising in connection with
a model for cholesteric liquid crystals. The principal feature of our study is
the assumption that the twist deformation of the nematic director incurs much
higher energy penalty than other modes of deformation. The appropriate ratio of
the elastic constants then gives a small parameter $\varepsilon$ entering an
Allen-Cahn-type energy functional augmented by a twist term. We consider the
behavior of the energy as $\varepsilon$ tends to zero. We demonstrate existence
of the local energy minimizers classified by their overall twist, find the
$\Gamma$-limit of the relaxed energies and show that it consists of the twist
and jump terms. Further, we extend our results to include the situation when
the cholesteric pitch vanishes along with $\varepsilon$.

Analysis of PDEs;Soft Condensed Matter