  A double-well energy expressed as a minimum of two quadratic functions,
called phase energies, is studied with taking into account the minimization of
the corresponding integral functional. Such integral, as being not sequentially
weakly lower semicontinuous, does not admit classical minimizers. To derive the
relaxation formula for the infimum, the minimizing sequence consisting of
solutions of convex problems appropriately approximating the original nonconvex
one is constructed. The weak limit of this sequence together with the weak
limit of the sequence of solutions of the corresponding dual problems and the
weak limits of the characteristic functions related to the phase energies are
involved in the relaxation formula.
