Hardy-Hodge Decomposition of Vector Fields in $Rn$
Complex Variables
2017-02-15 v1 Analysis of PDEs
Classical Analysis and ODEs
Abstract
We prove that a -valued vector field on IR n is the sum of the traces of two harmonic gradients, one in each component of , and of a -valued divergence free vector field. We apply this to the description of vanishing potentials in divergence form. The results are stated in terms of Clifford Hardy spaces, the structure of which is important for our study.
Keywords
Cite
@article{arxiv.1702.04233,
title = {Hardy-Hodge Decomposition of Vector Fields in $Rn$},
author = {Laurent Baratchart and Pei Dang and Tao Qian},
journal= {arXiv preprint arXiv:1702.04233},
year = {2017}
}
Comments
to appear in Transactions of the American Mathematical Society