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 with respect 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.
An optimal design problem with non-standard growth and no concentration effects / Barroso, Ana Cristina; Zappale, Elvira. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - (2021), pp. 1-28. [10.3233/ASY-211711]
An optimal design problem with non-standard growth and no concentration effects
Zappale, Elvira
2021
Abstract
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 with respect 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.| File | Dimensione | Formato | |
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