The ever-increasing interest in metamaterials, as well as the use of novel imaging technologies, calls for sound mathematical analysis of problems involving possibly irregular and sharply discontinuous anisotropies, resulting in mathematical descriptions involving the presence of multiple phases. In his PhD thesis of Samuele Ricco` ”Variational theories for multiphase problems in materials science and imaging”

focused on the study of five different questions stemming from materials science and imaging, with a combination of Gamma-convergence techniques, two-scale approaches, Regularity theory, fine properties of spaces of functions with bounded variations, Orlicz analysis, and Convex Integration.

Among the questions analyzed by Samuele Riccò, we single out the interplay between linearization and periodic microstructures for a model in magnetoelasticity, as well as the analysis of relaxation for a model in finite slip elastoplasticity allowing for two different elastic phases. This required a highly nontrivial combination of rank-one constructions, as well as the generalization to two-well settings of previous explicit constructions by S.Conti and G. Doltzmann.

He further established a higher integrability result for quasi-minimizers of double-phase functionals, introducing a new notion of infimal variational capacity and infimal fatness of sets, and proving equivalence of such notions to a corresponding Hardy and Poincarè inequalities, and characterized the effects of anisotropy for variational models in image reconstruction.

The thesis was evaluated by Prof. Elisa Davoli (TU Wien), Prof. Irene Fonseca (Carnegie Mellon University), and Prof. Marco Morandotti (Politecnico of Turin) and was unanimously evaluated with the best grade. Samuele will remain at our institute till the end of August. We wish him all the best for his future career!