Comptes Rendus
Partial differential equations
On a Liouville-type theorem for the Ginzburg–Landau system
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 903-905.

We prove that entire, complex valued solutions to the Ginzburg–Landau system with positive real and imaginary parts are constant in any spatial dimension. This property was shown very recently only in the planar case.

Nous prouvons que des solutions complexes au système de Ginzburg–Landau dans l'espace entier avec des parties réelles et imaginaires positives sont constantes dans toute dimension spatiale. Cette propriété a été démontrée très récemment, mais seulement dans le cas planaire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.001

Christos Sourdis 1

1 University of Athens, Greece
@article{CRMATH_2017__355_8_903_0,
     author = {Christos Sourdis},
     title = {On a {Liouville-type} theorem for the {Ginzburg{\textendash}Landau} system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {903--905},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.001},
     language = {en},
}
TY  - JOUR
AU  - Christos Sourdis
TI  - On a Liouville-type theorem for the Ginzburg–Landau system
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 903
EP  - 905
VL  - 355
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2017.07.001
LA  - en
ID  - CRMATH_2017__355_8_903_0
ER  - 
%0 Journal Article
%A Christos Sourdis
%T On a Liouville-type theorem for the Ginzburg–Landau system
%J Comptes Rendus. Mathématique
%D 2017
%P 903-905
%V 355
%N 8
%I Elsevier
%R 10.1016/j.crma.2017.07.001
%G en
%F CRMATH_2017__355_8_903_0
Christos Sourdis. On a Liouville-type theorem for the Ginzburg–Landau system. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 903-905. doi : 10.1016/j.crma.2017.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.001/

[1] F. Bethuel; H. Brezis; G. Orlandi Asymptotics for the Ginzburg–Landau equation in arbitrary dimensions, J. Funct. Anal., Volume 186 (2001), pp. 432-520

[2] H. Brezis Comments on two notes by L. Ma and X. Xu, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011), pp. 269-271

[3] L. Dupaigne; A. Farina Stable solutions of Δu=f(u) in RN, J. Eur. Math. Soc., Volume 12 (2010), pp. 855-882

[4] A. Farina; B. Sciunzi; N. Soave Monotonicity and rigidity of solutions to some elliptic systems with uniform limits | arXiv

[5] M. Fazly Rigidity results for stable solutions of symmetric systems, Proc. Amer. Math. Soc., Volume 143 (2015), pp. 5307-5321

[6] E. Sandier; I. Shafrir Small energy Ginzburg–Landau minimizers in R3 | arXiv

Cited by Sources:

Comments - Policy