Inserted: 3 jul 2020
Last Updated: 15 jul 2020
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 pe- nalization. Under our hypotheses, the integral representation includes a term which is absolutely continuous with respect to the Lebesgue measure and a perimeter term, but no additional singular term. We also provide an application to the modelling of thin lms.