Calculus of Variations and Geometric Measure Theory

J. M. Ball - G. Canevari - B. Stroffolini

A free discontinuity model for smectic thin films

created by canevari on 10 Mar 2023



Inserted: 10 mar 2023

Year: 2022

ArXiv: 2211.11051 PDF


We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free energy functional contains an interfacial energy which penalizes dislocations of the smectic layers at the jump. We discuss mathematical issues related to the existence of minimizers and provide examples of minimizers in some simplified settings.