2025/04/21 by Ana Cristina Barroso, Barroso, A. C., José Matías +3 · 1 citation
Engineering · #46E30 #49J45 #74A60 #74B20 #74M99 #Analysis of PDEs (math.AP) #Composite Structure Analysis and Optimization #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2504.15443
openalex publication_date 2025/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.