A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for regular configurations. The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy. Some first regularity results are presented for energetically-optimal film profiles.

中文翻译：

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异质外延薄膜模型的推导

刚性基板上外延应变薄膜的变分模型是通过 {\Gamma} 来自过渡层设置的收敛，以及通过文献中可用的用于规则配置的尖锐界面描述的弛豫来推导出来的。该模型的特点是配置能量可以解释导致薄膜形状的两种竞争机制。一方面，薄膜和基板之间的晶格失配会产生很大的应力，并且由于薄膜原子移动以释放弹性能，因此可能会出现波纹。另一方面，更平坦的轮廓可能是优选的以最小化表面能。给出了能量最佳薄膜轮廓的一些第一规律结果。