An optimal design problem with non-standard growth and no concentration effects

Article type: Research Article

Authors: Barroso, Ana Cristina^{a; *} | Zappale, Elvira^b

Affiliations: [a] Departamento de Matemática and CMAFcIO, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, Piso 1, 1749-016 Lisboa, Portugal | [b] Dipartimento di Science di Base ed Applicate per l’Ingegneria, Sapienza – Università di Roma, Via Antonio Scarpa, 16, 00161 Roma (RM), Italy

Correspondence: [*] Corresponding author. E-mail: acbarroso@ciencias.ulisboa.pt.

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.

Keywords: Non-standard growth conditions, optimal design, damage, dimension reduction, thin films, sets of finite perimeter, convexity

DOI: 10.3233/ASY-211711

Journal: Asymptotic Analysis, vol. 128, no. 3, pp. 385-412, 2022