Lifting of $\mathbb{RP}^{d-1}$-valued maps in $BV$. Applications to uniaxial $Q$-tensors

Radu Ignat, Xavier Lamy

Published 2017-06-05Version 1

We prove that a $BV$ map with values into the projective space $\mathbb{RP}^{d-1}$ has a $BV$ lifting with values into the unit sphere $\mathbb S^{d-1}$ that satisfies an optimal estimate of the $BV$ seminorm. As an application to liquid crystals, this result is also stated for $BV$ maps with values into the set of uniaxial $Q$-tensors.