On sequences of maps into \(S^1\) with equibounded \(W^{1/2}\) energies
For a bounded simply connected domain in \(\mathbb{R}^n\) with smooth boundary the authors consider bounded sequences in the fractional Sobolev space \[ W^{1/2}(\Omega, S^1):= \{u\in W^{1/2}(\Omega\times \mathbb{R}^2):|u|= 1\text{ a.e.}\} \] and characterize weak limits of subsequences in the framework of Cartesian currents.
scientific article; zbMATH DE number 2138514
scientific article