On the structure of the Sobolev space H1/2 with values into the circle

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How to recognize constant functions. Connections with Sobolev spaces (2002, background): “CONNECTIONS WITH SOBOLEV SPACES Häım Brezis Dedicated to Mark Visik with esteem and friendship”
Limiting Behavior of the Ginzburg–Landau Functional (2002, result): “Similar results are found in the work of Giaquinta, Modica, and Soou$ c cek on Cartesian currents [15] and analog of this result in the space H 1=2 is proven by Bourgain et al. [ 7 ].”
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.”
The Jacobian determinant revisited (2011, background): “Mironescu [6] (see also [7]) concerning maps in H 1 2 (Ω,S1) where Ω is the boundary of a domain in R3.”
Variational convergence for functionals of Ginzburg-Landau type. (2005, unknown): “(5.2)”