Hardy-Hodge Decomposition of Vector Fields in R$^{n}$

Laurent Baratchart (1) , Pei Dang (2) , Tao Qian (3)

1 FACTAS - Analyse fonctionnelle pour la conception et l'analyse de systèmes
2 MUST - Macau University of Science and Technology
3 UMac - University of Macau

We prove that a R^(n+1)-valued vector field on R^n is the sum of the traces of two harmonic gradients, one in each component of R^(n+1) \ R^n , and of a R^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.

Mots clés: quaternionic analysis; vector field decomposition; harmonic gradients

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Laurent Baratchart, Pei Dang, Tao Qian. Hardy-Hodge Decomposition of Vector Fields in R$^{n}$. Transactions of the American Mathematical Society, 2018, 370 (3), pp.2005 - 2022. ⟨10.1090/tran/7202⟩. ⟨hal-01462960⟩