An integrability result for $L^p$-vectorfields in the plane

Details An integrability result for $L^p$-vectorfields in the plane An integrability result for $L^p$-vectorfields in the plane

2010-07-05

arxiv.org/abs/1007.0681v3

Mathematics

Analysis of PDEs

16 pages, some typing errors fixed

Scientific paper

We prove that if $p>1$ then the divergence of a $L^p$-vectorfield $V$ on a
2-dimensional domain $\Omega$ is the boundary of an integral 1-current, if and
only if $V$ can be represented as the rotated gradient $\nabla^\perp u$ for a
$W^{1,p}$-map $u:\Omega\to S^1$. Such result extends to exponents $p>1$ the
result on distributional Jacobians of Alberti, Baldo, Orlandi.

Affiliated with

Also associated with

No associations

Rating

An integrability result for $L^p$-vectorfields in the plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An integrability result for $L^p$-vectorfields in the plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An integrability result for $L^p$-vectorfields in the plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-595340