  We consider the behavior of generalized Laplacian vector fields on a Jordan
domain of $\mathbb{R}^{3}$ with fractal boundary. Our approach is based on
properties of the Teodorescu transform and suitable extension of the vector
fields. Specifically, the present article addresses the decomposition problem
of a H\"older continuous vector field on the boundary (also called
reconstruction problem) into the sum of two generalized Laplacian vector fields
in the domain and in the complement of its closure, respectively. In addition,
conditions on a H\"older continuous vector field on the boundary to be the
trace of a generalized Laplacian vector field in the domain are also
established.
