(eng): For an integral functional defined on functions (u, v) ∈ W1,1 × L1 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.