Calculus of Variations and Geometric Measure Theory
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G. Canevari - G. Orlandi

Improved partial regularity for manifold-constrained minimisers of subquadratic energies

created by orlandi on 19 Dec 2018


Submitted Paper

Inserted: 19 dec 2018

Pages: 13
Year: 2018

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.

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