A novel general framework for the study of \(\Gamma \)-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the \(\Gamma \)-limit of these kind of functionals by knowing the \( \Gamma \)-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.

中文翻译：

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关于成对的度量和能量度量定义的泛函的伽玛收敛

介绍了一种新颖的通用框架，用于研究在度量对和能量度量对上定义的函数的（\ Gamma \）收敛。该理论使我们能够通过了解基本能量的\（\ Gamma \）-极限来确定这类功能的\（\ Gamma \）-极限。特别地，在弛豫过程中的附加作用中，导致官能团与基础能量之间的相互作用，在后者聚合为非连续能量的情况下。这项研究的动机是在一个带有原子的外延生长演化的背景下提出的问题。还介绍了应用通用理论的有趣案例。