abstract 85

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

85

A class of harmonic differential forms

Alberto Cialdea

We introduce a class of harmonic differential forms. It consists of the $k$-forms $u$ defined in a domain ${\Omega}$ such that $u$, $*u$, ${\delta} u$ and $*d u$ do exist on ${\partial}{\Omega}$ in a weak sense and their coefficients are in $L^{p}({\partial}{\Omega})$. We prove that a form belongs to this space if and only if it can be written as a "simple layer" potential with $L^p$ densities. We obtain a regularization theorem on the boundary and some uniqueness properties. We give also the relevant Calderón projector.

Keywords: Harmonic differential forms; uniqueness theorems; potential theory; Calderón projector.

Cite this paper:

Cialdea A. 

A class of harmonic differential forms.

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 11, No.1 pp.161-186, 2023.