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

Reference39 articles.

1. Relaxation of convex functionals: The gap problem;Acerbi;Ann. Inst. H. Poincaré Anal. Non Linéaire,2003

2. Minimizers for a double-well problem with affine boundary conditions;Allaire;Proc. Royal Soc. Edinburgh,1999

3. An optimal design problem with perimeter penalization;Ambrosio;Calc. Var. Partial Differential Equations,1993

4. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, 2000.

5. Concentration versus Oscillation Effects in Brittle Damage

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Relaxation for an optimal design problem in BD(Ω);Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2022-03-10