Lemma Poincar\'e for L_infty,loc - forms

TL;DR

This paper proves that every closed L_infty,loc - form on R^n is exact, establishing a version of the Poincaré lemma in the L_infty,loc setting using currents, without geometric constructions.

Contribution

It extends the classical Poincaré lemma to closed L_infty,loc - forms on R^n, showing they are exact via a proof that avoids explicit geometric methods.

Findings

Every closed L_infty,loc - form on R^n is exact.

De Rham theorem holds in the L_infty,loc context.

Proof does not rely on explicit geometric constructions.

Abstract

We show that every closed L_infty,loc - form on R^n is exact. Differential is understood in the sense of currents. The proof does not use any explicit geometric constructions. De Rham theorem follows.