An optimal design problem with non-standard growth and no concentration effects-Reference-Cited by-同舟云学术

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

Published:2021-05-31 Issue: Volume: Page:1-28
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Barroso Ana Cristina¹,Zappale Elvira²

Affiliation:

1. Departamento de Matemática and CMAFcIO, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, Piso 1, 1749-016 Lisboa, Portugal. E-mail: acbarroso@ciencias.ulisboa.pt

2. Dipartimento di Science di Base ed Applicate per l’Ingegneria, Sapienza – Università di Roma, Via Antonio Scarpa, 16, 00161 Roma (RM), Italy. E-mail: elvira.zappale@uniroma1.it

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.

Publisher

IOS Press

Subject

General Mathematics

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