L¹-Poincar\'e and Sobolev inequalities for differential forms in Euclidean spaces
classification
🧮 math.DG
keywords
inequalitiesdifferentialformspoincarsobolevbackbourgain-brezisestimates
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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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