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1 results

Relaxation for an optimal design problem in BD(Ω)
Part of
- Manifolds
- Existence theories
Ana Cristina Barroso, José Matias, Elvira Zappale
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 3 / June 2023

Published online by Cambridge University Press:

10 March 2022, pp. 721-763

Print publication:

June 2023
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We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair $(\chi,u)$, where $\chi$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded deformation, of an energy with a bulk term depending on the symmetrized gradient as well as a perimeter term.