Multi-level structured deformations: relaxation via a global method approach

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.