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Power Law Approximation Results for Optimal Design Problems

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Nonlinear Differential Equations and Applications (PICNDEA 2022)

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 7))

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Abstract

In this note, we show some results related to power law approximations for optimal design and damaging problems. The asymptotics, via \(\Gamma \)-convergence, leads to supremal functionals whose densities are related to the original ones via suitable asymptotic minimum problems. Some properties of these limiting energy densities are also proven.

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Acknowledgements

EZ is a member of INdAM - GNAMPA whose support is gratefully acknowledged. VS acknowledges the support of Sapienza through “Programma Professori Visitatori in condizione di rischio a causa di conflitti anno 2022” and “INdAM Programma Sportello Ucraina”.

Author information

Authors and Affiliations

  1. Dipartimento di Scienze e Tecnologie, Universitá degli studi del Sannio, Benevento, Italy

    Giuliano Gargiulo

  2. Head of Department at Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Valerii Samoilenko

  3. Dipartimento di Scienze di Base ed Applicate per l’Ingengeria, Sapienza – Università di Roma, Rome, Italy

    Elvira Zappale

  4. CIMA – Centro de Investigacao em Matematica e Aplicacoes, Univesidade de Evora, Évora, Portugal

    Elvira Zappale

Authors
  1. Giuliano Gargiulo
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  2. Valerii Samoilenko
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  3. Elvira Zappale
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Corresponding author

Correspondence to Elvira Zappale .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Pisa, Pisa, Italy

    Hugo Beirão da Veiga

  2. Department of Mathematics, Centro de Investigação em Matemática e Aplicações (CIMA), University of Évora, Évora, Portugal

    Feliz Minhós

  3. Department of Mathematics, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

    Nicolas Van Goethem

  4. Department of Mathematics, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

    Luís Sanchez Rodrigues

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Gargiulo, G., Samoilenko, V., Zappale, E. (2024). Power Law Approximation Results for Optimal Design Problems. In: Beirão da Veiga, H., Minhós, F., Van Goethem, N., Sanchez Rodrigues, L. (eds) Nonlinear Differential Equations and Applications. PICNDEA 2022. CIM Series in Mathematical Sciences, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-031-53740-0_6

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