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arXiv:1902.10138 [math.DG]AbstractReferencesReviewsResources

$L^1$-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces

Annalisa Baldi, Bruno Franchi, Pierre Pansu

Published 2019-02-26Version 1

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.

Comments: Accepted for publication in Science China Mathematics. arXiv admin note: text overlap with arXiv:1902.04819
Categories: math.DG
Subjects: 58A10, 26D15, 46E35
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