  For an integral functional defined on functions $(u,v)\in W^{1,1}\times L^1$
featuring a prototypical strong interaction term between $u$ and $v$, we
calculate its relaxation in the space of functions with bounded variations and
Radon measures. Interplay between measures and discontinuities bring various
additional difficulties, and concentration effects in recovery sequences play a
major role for the relaxed functional even if the limit measures are absolutely
continuous with respect to the Lebesgue one.
