Decomposition of $L^2$-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

L. Baratchart, C. Gerhards, A. Kegeles

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in ${\mathbb{R}}^d$ with $d\ge 3$, we prove that any field $f\in L^{2} (\partial Ω; \mathbb{R}^{d…