On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures

A novel general framework for the study of Γ -convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the Γ -limit of these kind of functionals by knowing the Γ -limit of the underlying energies. In particular, the interaction between the functionals and the underlying energies results, in the case these latter converge to a non-continuous energy, in an additional effect in the relaxation process. This study was motivated by a question in the context of epitaxial growth evolution with adatoms. Interesting cases of application of the general theory are also presented.