On the potential of a solenoidal vector field
The author constructs one solution to rot u\(=f\) in an unbounded domain (star shaped with respect to a sphere) for a differentiable vector field f (not necessarily vanishing at infinity) provided the necessary conditions div f\(=0\), \(\int_{S}f\cdot \nu =0\) (if S is an interval boundary part) hold. Necessary and sufficient conditions for solving rot u\(=f\in L_ p\) with \(u|_{\partial G}=0\) for bounded and (if \(p<3)\) unbounded domains of a more difficult structure by means of potential theory can be found e.g. in \textit{W. von Wahl} [Lect. Notes Math. 1431, 152-157 (1990; Zbl 0719.35015)].
scientific article; zbMATH DE number 4200715