Helmholtz's theorem when the domain is infinite and when the field has singular points
Ruth Gregory · The Quarterly Journal of Mechanics and Applied Mathematics · 1996
A direct proof, based on classical analysis, is given to extend Helmholtz's fundamental theorem of vector analysis to cases in which the domain is infinite and/or the field u(r) has isolated singular points. No restriction whatsoever is placed upon the growth of u(r) as ‖r‖⇒∝, or as the singular points are approached. Consequently all representation theorems dependent upon Helmholtz's theorem are also freed from such restrictions