Relaxation for Optimal Design Problems with Non-standard Growth

  • Ana Cristina Barroso
  • Elvira ZappaleEmail author


In this paper we investigate the possibility of obtaining a measure representation for functionals arising in the context of optimal design problems under non-standard growth conditions and perimeter penalization. Applications to modelling of strings are also provided.


Measure representation Non-standard growth conditions Optimal design Sets of finite perimeter Convexity 

Mathematics Subject Classification

49J45 74K10 



The authors would like to thank CMAF-CIO at the Universidade de Lisboa, CIMA at the Universidade de Évora and Dipartimento di Ingegneria Industriale at the Università degli Studi di Salerno, where this research was carried out. We also gratefully acknowledge the support of INDAM GNAMPA, Programma Professori Visitatori 2017. The research of ACB and EZ was partially supported by the Fundação para a Ciência e a Tecnologia through Project UID/MAT/04561/2013 and project UID/MAT/04674/2013, respectively.


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Authors and Affiliations

  1. 1.Departamento de Matemática and CMAFIOFaculdade de Ciências da Universidade de LisboaLisbonPortugal
  2. 2.Dipartimento di Ingegneria IndustrialeUniversità degli Studi di SalernoFiscianoItaly
  3. 3.CIMA (Universidade de Évora)ÉvoraPortugal

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