Relaxation for Optimal Design Problems with Non-standard Growth

Abstract

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.

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Acknowledgements

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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Correspondence to Elvira Zappale.

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This paper is dedicated to the memory of our good friend and colleague Graça Carita, with whom the second author had the privilege of collaborating on many previous occasions. Graça joined us at the early stages of this work and tragically passed away on September 26, 2016.

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Barroso, A.C., Zappale, E. Relaxation for Optimal Design Problems with Non-standard Growth. Appl Math Optim 80, 515–546 (2019). https://doi.org/10.1007/s00245-017-9473-6

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Keywords

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

Mathematics Subject Classification

  • 49J45
  • 74K10