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

Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities