Integral representation for a relaxed optimal design problem for non-simple grade two materials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913631426314240 |
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| author | Barroso, Ana Cristina Zappale, Elvira |
| author_facet | Barroso, Ana Cristina Zappale, Elvira |
| contents | A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained.
Departing from an energy with a bulk term depending on the deformation gradient and its derivatives, as well as a perimeter term, the functional in question corresponds to the relaxation of this energy with respect to a pair $(χ,u)$, where $χ$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded hessian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral representation for a relaxed optimal design problem for non-simple grade two materials Barroso, Ana Cristina Zappale, Elvira Analysis of PDEs Optimization and Control 49J45, 49Q20, 26B25 A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and its derivatives, as well as a perimeter term, the functional in question corresponds to the relaxation of this energy with respect to a pair $(χ,u)$, where $χ$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded hessian. |
| title | Integral representation for a relaxed optimal design problem for non-simple grade two materials |
| topic | Analysis of PDEs Optimization and Control 49J45, 49Q20, 26B25 |
| url | https://arxiv.org/abs/2412.16027 |