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arXiv · 1902.10138

$L^1$-Poincar\'e and Sobolev inequalities for differential forms in Euclidean spaces

Annalisa Baldi·Bruno Franchi·Pierre Pansu
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Abstract

In this paper, we prove Poincar\'e and Sobolev inequalities for differential forms in $L^1(\mathbb R^n)$. The singular integral estimates that it is possible to use for $L^p$, $p>1$, are replaced here with inequalities which go back to Bourgain-Brezis.

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Annalisa Baldi, Bruno Franchi, Pierre Pansu. 2019-02-26. $L^1$-Poincar\'e and Sobolev inequalities for differential forms in Euclidean spaces. https://arxiv.org/abs/1902.10138

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