On a Fractional Ginzburg-Landau Equation and 1/2-Harmonic Maps into Spheres
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0776-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0776-3 | ||
| 245 | 0 | 0 | |a On a Fractional Ginzburg-Landau Equation and 1/2-Harmonic Maps into Spheres |h [Elektronische Daten] |c [Vincent Millot, Yannick Sire] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Millot |D Vincent |u Laboratoire J.-L. Lions (CNRS UMR 7598), Université Paris Diderot-Paris 7, Paris, France |4 aut | |
| 700 | 1 | |a Sire |D Yannick |u Laboratoire d'Analyse, Topologie, Probabilités (CNRS UMR 7353), Université Aix-Marseille, Marseille, France |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/1(2015-01-01), 125-210 |x 0003-9527 |q 215:1<125 |1 2015 |2 215 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0776-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0776-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Millot |D Vincent |u Laboratoire J.-L. Lions (CNRS UMR 7598), Université Paris Diderot-Paris 7, Paris, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Sire |D Yannick |u Laboratoire d'Analyse, Topologie, Probabilités (CNRS UMR 7353), Université Aix-Marseille, Marseille, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/1(2015-01-01), 125-210 |x 0003-9527 |q 215:1<125 |1 2015 |2 215 |o 205 | ||