  According to a continuous medium theory, in very thin ferroelectric films
with real metallic electrodes (or dead layers near the electrodes) the domain
structure reduces to sinusoidal distribution of ferroelectric polarization.
Such a sinusoidal structure was considered in 1980s for para-ferroelectric
phase transition in a capacitor with dead layers near electrode. We give a
review of this theory and its further development for the case of real metallic
electrodes. The goal of the general theory is to consistently interpret the
experimental data in very thin films with real metallic electrodes. This is
illustrated on a recent experimental data for 5-30 nm BaTiO3 films with
SrRuO3/SrTiO3 electrodes. The screening length by real metallic electrodes is
very small small (<1A), but it has a profound effect on ferroelectric
properties and its phase behavior. This general theory also allows to formulate
the important open problems and show paths towards their solution. In
particular, this is a problem of finding parameters of the system, which can
sustain the ferroelectric memory over a desired lifetime.
