caa a22 4500 605515190 CHVBK 20210128100708.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00205-014-0776-3 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0776-3 On a Fractional Ginzburg-Landau Equation and 1/2-Harmonic Maps into Spheres [Elektronische Daten] [Vincent Millot, Yannick Sire] This paper is devoted to the asymptotic analysis of a fractional version of the Ginzburg-Landau equation in bounded domains, where the Laplacian is replaced by an integro-differential operator related to the square root Laplacian as defined in Fourier space. In the singular limit $${\varepsilon \to 0}$$ ε → 0 , we show that solutions with uniformly bounded energy converge weakly to sphere valued 1/2-harmonic maps, that is, the fractional analogues of the usual harmonic maps. In addition, the convergence holds in smooth functions spaces away from a countably $${\fancyscript{H}^{n-1}}$$ H n - 1 -rectifiable closed set of finite (n−1)-Hausdorff measure. The proof relies on the representation of the square root Laplacian as a Dirichlet-to-Neumann operator in one more dimension, and on the analysis of a boundary version of the Ginzburg-Landau equation. Besides the analysis of the fractional Ginzburg-Landau equation, we also give a general partial regularity result for stationary 1/2-harmonic maps in an arbitrary dimension. Springer-Verlag Berlin Heidelberg, 2014 Millot Vincent Laboratoire J.-L. Lions (CNRS UMR 7598), Université Paris Diderot-Paris 7, Paris, France aut Sire Yannick Laboratoire d'Analyse, Topologie, Probabilités (CNRS UMR 7353), Université Aix-Marseille, Marseille, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 125-210 0003-9527 215:1<125 2015 215 205 https://doi.org/10.1007/s00205-014-0776-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0776-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Millot Vincent Laboratoire J.-L. Lions (CNRS UMR 7598), Université Paris Diderot-Paris 7, Paris, France aut NATIONALLICENCE 700 1- Sire Yannick Laboratoire d'Analyse, Topologie, Probabilités (CNRS UMR 7353), Université Aix-Marseille, Marseille, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 125-210 0003-9527 215:1<125 2015 215 205