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 - <p style="text-align: justify;">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.<br/>Some applications to specific relaxation problems are also mentioned, showing
that our global method approach recovers some previously established results.</p>