  We attempt to describe surface defects in smectic A thin films by formulating
a free discontinuity problem - that is, a variational problem in which the
order parameter is allowed to have jump discontinuities on some (unknown) set.
The free energy functional contains an interfacial energy which penalizes
dislocations of the smectic layers at the jump. We discuss mathematical issues
related to the existence of minimizers and provide examples of minimizers in
some simplified settings.
