We obtain an integral representation for certain functionals arising in the context of optimal design and damage evolution problems under non-standard growth conditions and perimeter penalisation. Under our hypotheses, the integral representation includes a term which is absolutely continuous withrespect to the Lebesgue measure and a perimeter term, but no additional singular term. We also study some dimension reduction problems providing results for the optimal design of thin films.

中文翻译：

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一个非标准生长且无浓度效应的优化设计问题

我们获得了在非标准生长条件和周长惩罚下优化设计和损伤演化问题背景下出现的某些功能的积分表示。在我们的假设下，积分表示包括一个关于 Lebesgue 测度绝对连续的项和一个周长项，但没有额外的单项。我们还研究了一些降维问题，为薄膜的优化设计提供了结果。