A note on div curl inequalities

By Loredana Lanzani, E. Stein. 2005

74 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/49875bc0f00fc0a58b595b501544c2ac5362dde5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

New estimates for elliptic equations and Hodge type systems (2007, methodology): “The weaker assertion (3.12) of Corollary 17 was obtained independently by Lanzani and Stein [7] with an elementary approach in the spirit of [14].”
Hardy-Sobolev inequalities for vector fields and canceling linear differential operators (2013, background): “Stein [6, 7, 17] (see also [4, 5, 8, 27,28]) and the Korn–Sobolev inequality [25].”
Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations (2014, background): “1 and the classical elliptic regularity theory, we have a Gagliardo–Nirenberg–Sobolev inequality for differential forms [16, Corollary 17] (see also [63]): if ∈ {2, .”
Limiting Sobolev inequalities for vector fields and canceling linear differential operators (2011, background): “128-129], the Korn–Sobolev inequality [38] and which is a modiVcation of an argument for estimates of circulation along closed curves [40], divergence-free vector Velds [41], closed diUerential forms [26] and vector Velds that satisfy a second-order condition [42].”
Estimates for L-1 vector fields under higher-order differential conditions (2008, background): “When n ≥ 4, there are intermediate interesting inequalities for k-forms with 2 ≤ k ≤ n − 2 [6, 4].”
Semi-classical states for the Choquard equation (2013, background): “th space divergence-free data [35]. As a consequence of theorem 1 and the classical elliptic regularity theory, we have a Gagliardo–Nirenberg–Sobolev inequality for forms [16, corollary 17] (see also [63]): if ℓ∈ {2,...,n−2}, then (1.5) kukLn/(n−1) ≤ C kdukL1 +kd∗ukL1 ; the inequality still holds fo”