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Relaxation for an optimal design problem with linear growth and perimeter penalization

Published online by Cambridge University Press:  02 April 2015

Graça Carita  and
Elvira Zappale
Graça Carita
Affiliation:
Departamento de Matemática, Centro de Investigação em Matemática e Aplicações, Universidade de Évora, Rua Romão Ramalho, 59 7000-671 Évora, Portugal, (gcarita@uevora.pt)
Elvira Zappale
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Salerno, Italy, (ezappale@unisa.it)
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Abstract

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This paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in order to avoid non-existence of admissible solutions and, in addition, this leads to an interaction in the limit energy. More general models have also been taken into account.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 2 , April 2015 , pp. 223 - 268
Copyright
Copyright © Royal Society of Edinburgh 2015