H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg–Landau equation

By Jean Bourgain, Haim Brezis, Petru Mironescu. 2004

127 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1fadffb69db4e7f2c07a540e83a35c8a10c9660f

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Embeddings for A-weakly differentiable functions on domains (2017, background): “This and substantial contributions in [8, 9, 10, 4, 6, 5, 7, 48, 49, 50, 51] lead to the remarkable characterization by Van Schaftingen [52] of all k–homogeneous linear differential operators A such that ‖Du‖L1∗ (Rn) 6 c‖Au‖L1(Rn) (1.”
Estimates for L-1 vector fields under higher-order differential conditions (2008, methodology): “The proof of Section 4 uses the tools of [3, 4] that trace back to [2, 5].”
A note on div curl inequalities (2005, background): “Brezis, Mironescu, and Van Schaftingen, [1],[2],[ 3 ],[7], that involve the divergence and curl of vector fields.”
The Jacobian determinant revisited (2011, background): “Mironescu [6] (see also [7]) concerning maps in H 1 2 ( ,S1) where is the boundary of a domain in R3.”
New estimates for elliptic equations and Hodge type systems (2007, methodology): “This can be proved by the same argument as in [4], [5], or by the argument due to Van Schaftingen [13], [14].”
Lifting, degree, and distributional Jacobian revisited (2005, methodology): “15) is a straightforward adaptation—left to the reader— of the proof of theorem 1 in [9].”
Hardy-Sobolev inequalities for vector fields and canceling linear differential operators (2013, background): “ling if \ ξ∈Rn\{0} A(ξ)[V] = {0}. Theorem 1 covers in particular the classical inequality (1.1), the Hodge– Sobolev inequality of J.Bourgain and H.Brezis, and L.Lanzani and E.Stein [6,7,17] (see also [4,5,8,27,28]) and the Korn–Sobolev inequality [25]. In the present work we continue this programme ”