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arXiv · 1810.12025

Improved partial regularity for manifold-constrained minimisers of subquadratic energies

Giacomo Canevari·Giandomenico Orlandi
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Abstract

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.

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Giacomo Canevari, Giandomenico Orlandi. 2018-10-29. Improved partial regularity for manifold-constrained minimisers of subquadratic energies. https://arxiv.org/abs/1810.12025

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