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Volume 4, Issue 3
Multi-Level Structured Deformations: Relaxation via a Global Method Approach

Ana Cristina Barroso, José Matias & Elvira Zappale

DOI: 10.4208/cmaa.2025-0010

Commun. Math. Anal. Appl., 4 (2025), pp. 368-391.

Published online: 2025-09

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  • Abstract

We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an integral representation result for an abstract class of variational functionals in this framework via a global method for relaxation and identify, under quite general assumptions, the corresponding relaxed energy densities through the study of a related local Dirichlet-type problem.
Some applications to specific relaxation problems are also mentioned, showing that our global method approach recovers some previously established results.

  • Keywords

Global method for relaxation, hierarchical system of structured deformations, multi-scale geometry, disarrangements, integral representation.

  • AMS Subject Headings

49J45, 46E30, 74A60, 74M99, 74B20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-4-368, author = {Barroso , Ana CristinaMatias , José and Zappale , Elvira}, title = {Multi-Level Structured Deformations: Relaxation via a Global Method Approach}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {3}, pages = {368--391}, abstract = {

We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an integral representation result for an abstract class of variational functionals in this framework via a global method for relaxation and identify, under quite general assumptions, the corresponding relaxed energy densities through the study of a related local Dirichlet-type problem.
Some applications to specific relaxation problems are also mentioned, showing that our global method approach recovers some previously established results.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0010}, url = {http://global-sci.org/intro/article_detail/cmaa/24334.html} }
TY - JOUR T1 - Multi-Level Structured Deformations: Relaxation via a Global Method Approach AU - Barroso , Ana Cristina AU - Matias , José AU - Zappale , Elvira JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 368 EP - 391 PY - 2025 DA - 2025/09 SN - 4 DO - http://doi.org/10.4208/cmaa.2025-0010 UR - https://global-sci.org/intro/article_detail/cmaa/24334.html KW - Global method for relaxation, hierarchical system of structured deformations, multi-scale geometry, disarrangements, integral representation. AB -

We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an integral representation result for an abstract class of variational functionals in this framework via a global method for relaxation and identify, under quite general assumptions, the corresponding relaxed energy densities through the study of a related local Dirichlet-type problem.
Some applications to specific relaxation problems are also mentioned, showing that our global method approach recovers some previously established results.

Barroso , Ana CristinaMatias , José and Zappale , Elvira. (2025). Multi-Level Structured Deformations: Relaxation via a Global Method Approach. Communications in Mathematical Analysis and Applications. 4 (3). 368-391. doi:10.4208/cmaa.2025-0010
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