# On Poincaré and de Rham‘s theorems

Mardare, S (2008). On Poincaré and de Rham‘s theorems. Revue Roumaine de Mathématiques Pures et Appliquées, 53(5-6):523-541.

## Abstract

We prove Poincaré's theorem under general assumptions on the data. Then we derive the regularity of the solution from a result of Borchers and Sohr [6]. Finally, we give an elementary proof of the de Rham's theorem in the case of 1-dimensional flows on the Euclidean space by applying the techniques introduced in the proof of Poincaré's theorem.

## Abstract

We prove Poincaré's theorem under general assumptions on the data. Then we derive the regularity of the solution from a result of Borchers and Sohr [6]. Finally, we give an elementary proof of the de Rham's theorem in the case of 1-dimensional flows on the Euclidean space by applying the techniques introduced in the proof of Poincaré's theorem.