  This paper describes several different formulations of the so-called
"cellular problem" which is a system of partial differential equations arising
in the theory of homogenization, subject to periodicity boundary conditions.
Variational formulations of the cellular problem are presented where the main
unknown is the displacement, the stress or the strain, as well as several
different formulations as minimization problems. Two dual formulations are also
presented, one in displacement-stress and another one in strain-stress. The
corresponding Lagrangians may be used in numerical optimization algorithms
based on alternated directions.
