Higher Dimensional Generalization of Helmholtz Theorem We know that given the divergence and curl of a vector field (and appropriate boundary conditions) it is possible to construct a unique vector field in $\mathbb R^3$.  The specific problem I am thinking about is related to the PDE
$$\operatorname{div} F = g,$$
where $F \colon \mathbb R^n \to \mathbb R^n$ is a vector field and $g \colon \mathbb R^n \to \mathbb R$ is a scalar field, and $\operatorname{div}$ is the $n$-dimensional generalization of the divergence given by
$$\operatorname{div} F = \frac{dF_{i}}{dx_{i}}$$
(summation implied). What additional pieces of information are necessary to uniquely specify $F$ given the function $g$ (we know the answer is the curl of $F$ in 3D)?

I read that W. Hauser generalized Helmholtz's theorem to R⁴ by proving it for second-rank tensors [1,2]. but unfortunately I could not found his original papers for download (to see the details).. tray by yourself to found these references, you may be more lucky than me:
[1] W. Hauser, "On the Fundamental Equations of Electromagnetism," Am. J. Physics, vol. 38, no. 1, pp. 80-85, 1970.
[2] W. Hauser, Introduction to the Principles of Electromagnetism. Addison-Wesley Educational Publishers Inc, 1971.
