On Professor Grioli’s last riddle: What boundary and initial conditions make sense for microstructured continua?

Abstract

An abridged but faithful exposition of Professor Grioli’s version of the theory of microstructured continua of Cosserat type is given, so as to reformulate and discuss the title question. This exposition prompts some reflections on how to bridge by the use of continuum theories the gap between microscopic and macroscopic mathematical descriptions of matter.