Calculus of Variations and Geometric Measure Theory

G. Canevari - G. Orlandi

Improved partial regularity for manifold-constrained minimisers of subquadratic energies

created by orlandi on 19 Dec 2018
modified by canevari on 29 Jan 2021


Accepted Paper

Inserted: 19 dec 2018
Last Updated: 29 jan 2021

Journal: Communications in Mathematical Physics
Volume: 374
Number: 2020
Pages: 1483–1495
Year: 2020

ArXiv: 1810.12025 PDF


We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular set of such a map decomposes into a $1$-dimensional set, which can be physically interpreted as a non-orientable line defect, and a locally finite set, i.e. a collection of point defects.