English

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 IRn+1IR n+1-valued vector field on IR n is the sum of the traces of two harmonic gradients, one in each component of IRn+1 IRnIR n+1 \ IR n , and of a IRnIR n-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

R2 v1 2026-06-22T18:18:05.853Z