STOKES' THEOREM FOR DIFFERENTIAL FORMS OF AN ARBITRARY SUMMABILITY

Abstract

The work is devoted to the calculus of differential forms of Sobolev type. The authors of [2, 3] investigated a situation similar to the embedding theorem of Sobolev space W} into the space of continuous functions provided p > n, defined J_x и and established the Stokes' theorem j_x uu = du. In this paper we study the case corresponding to the embedding of W}, into the L_q provided p < n. In this case we give meaning to the integral of k-forms on k-dimensional oriented manifold, to be consistent with already existing theory. We set the Stokes' formula Jx и = du in the model case of X С К", dimX = n. The existence of the integral in the right hand side is understood in the sense described in this paper.