Let . If has zero integral, then the equation need not have a solution [6] or even [2]. Using these results, we prove that, whenever and , there exists some ℓ-form such that and the equation has no solution . This provides a negative answer to a question raised by Baldi, Franchi, and Pansu [1].
Soit . Si est d'intégrale nulle, alors en général il n'est pas possible de résoudre l'équation avec [6], ou même [2]. En utilisant ces résultats, nous prouvons que, pour et , il existe une ℓ-forme avec et telle que l'équation n'a pas de solution . Ceci donne une réponse négative à une question posée par Baldi, Franchi et Pansu [1].
Accepted:
Published online:
@article{CRMATH_2019__357_4_355_0, author = {Curc\u{a}, Eduard}, title = {On the representation as exterior differentials of closed forms with {\protect\emph{L}\protect\textsuperscript{1}-coefficients}}, journal = {Comptes Rendus. Math\'ematique}, pages = {355--359}, publisher = {Elsevier}, volume = {357}, number = {4}, year = {2019}, doi = {10.1016/j.crma.2019.04.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2019.04.011/} }
TY - JOUR AU - Curcă, Eduard TI - On the representation as exterior differentials of closed forms with L1-coefficients JO - Comptes Rendus. Mathématique PY - 2019 SP - 355 EP - 359 VL - 357 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2019.04.011/ DO - 10.1016/j.crma.2019.04.011 LA - en ID - CRMATH_2019__357_4_355_0 ER -
%0 Journal Article %A Curcă, Eduard %T On the representation as exterior differentials of closed forms with L1-coefficients %J Comptes Rendus. Mathématique %D 2019 %P 355-359 %V 357 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2019.04.011/ %R 10.1016/j.crma.2019.04.011 %G en %F CRMATH_2019__357_4_355_0
Curcă, Eduard. On the representation as exterior differentials of closed forms with L1-coefficients. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 355-359. doi : 10.1016/j.crma.2019.04.011. http://archive.numdam.org/articles/10.1016/j.crma.2019.04.011/
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