On Iterations of the Green Integrals and their Applications to Elliptic Differential Complexes

Convergence of iterations of special Green integrals for overdetermined elliptic linear partial differential operators P of order p ≥ 1 is proved. Using this result we obtain necessary and sufficient conditions for the solvability of the equation Pu = f in the Sobolev space W^p,²(D) and, as a corollary, necessary and sufficient conditions for the vanishing of the first cohomology group of elliptic differential complexes. Also a criterion for the solvability of a P-Neumann problem for elliptic differential operators is proved.