  We consider the Skorokhod problem in a time-varying interval. We prove
existence and uniqueness for the solution. We also express the solution in
terms of an explicit formula. Moving boundaries may generate singularities when
they touch. We establish two sets of sufficient conditions on the moving
boundaries that guarantee that the variation of the local time of the
associated reflected Brownian motion is, respectively, finite and infinite. We
also apply these results to study the semimartingale property of a class of
two-dimensional reflected Brownian motions.
