ON ITERATIONS OF THE GREEN INTEGRALS AND THEIR APPLICATIONS TO ELLIPTIC DIFFERENTIAL COMPLEXES

Convergence of iterations of special Green integrals for overdetermine d elliptic linear partial differential operators P of order p greater than or equal to 1 is proved. Using this result we obtain necessary an d sufficient conditions for the solvability of the equation Pu = f in the Sobolev space W-p,W-2(D) and, as a corollary, necessary and suffic ient conditions for the vanishing of the first cohomology group of ell iptic differential complexes. Also a criterion for the solvability of a P-Neumann problem for elliptic differential operators is proved.