  In this paper, we characterize all the distributions $F \in \mathcal{D}'(U)$
such that there exists a continuous weak solution $v \in C(U,\mathbb{C}^{n})$
(with $U \subset \Omega$) to the divergence-type equation
$$L_{1}^{*}v_{1}+...+L_{n}^{*}v_{n}=F,$$ where
$\left\{L_{1},\dots,L_{n}\right\}$ is an elliptic system of linearly
independent vector fields with smooth complex coefficients defined on $\Omega
\subset \mathbb{R}^{N}$. In case where $(L_1,\dots, L_n)$ is the usual gradient
field on $\mathbb{R}^N$, we recover the classical result for the divergence
equation proved by T. De Pauw and W. Pfeffer.
