The Poincare Generalized Lemma

Abstract

In this note we prove the result: let Ω be a non void opensubset ofRNandfak-generalized differential form on Ω. Moreover,assume that Ω is star-shaped and thatfis a closed form on Ω. Then,there is a (k−1)-generalized differential formuon Ω whose differentialisf.This result is a part of what I call internal development of theColombeau theory.