Abstract Let be the unit cube in , be Banach spaces and , the associate spaces of and . In this paper, we will show that the existence in , the space of all ‐dimensional fields in , of solutions of the equation for is closely related to the problem of obtaining a Sobolev‐type embedding , where is the Sobolev space of functions vanishing on the boundary whose gradient belongs to .
Manzo et al. (Fri,) studied this question.