MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Energetics of fine domain structures

Antonio DeSimone


In the last few decades, new mathematical tools have become available for the analysis of minimization problems involving non-convex free-energies. These advances have shed some new light on the behavior of a variety of physical systems exhibiting domain structures, and on their response to external actions (forces, electromagnetic fields, etc.). Examples range from ferroelastic solids (in particular, shape memory alloys) to ferromagnetic and ferroelectric materials (in particular, solids with strong electro- or magneto-elastic coupling). In this paper, striped domain patterns observed in liquid crystalline polymers are discussed, showing that the emergence of domain structures, and the success of the mathematical techniques for their analysis are not peculiar to crystalline solids.

elastomers, liquid crystals, calculus of variations, convexity

Related publications

1999 Repository Open Access
Antonio DeSimone

Energetics of fine domain structures

In: Ferroelectrics, 222 (1999) 1-4, pp. 533-542