Characterization of the gradient of a distribution
d Abstract. Let ß be an open subset of IR" and let S, , . . . ,S . be distributions on Q. Then the system — U dxj = Si , . .., -— U = S„k solvable if and only if the equation ^ Si(i/',) = 0 holds for every testing field = (i/'i,. . .,tj/„) with V ^ = 0. Using elementary arguments of distribution theory (the testing functions needed are represented as the divergence of appropriate vector fields) a constructive proof of this Statement is given.