Geodesic
Quantitative, uniqueness, and vortex degree estimates for solutions of the Ginzburg-Landau equation
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we provide a sharp upper bound for the maximal order of vanishing for non-minimizing solutions of the Ginzburg-Landau equation $$ \Delta u=-{1\over\epsilon^2}(1-|u|^2)u $$ which improves our previous result [12]. An application of this result is a sharp upper bound for the degree of any vortex. We treat Dirichlet (homogeneous and non-homogeneous) as well as Neumann boundary conditions.
Classification : 35B05, 35J25, 35J60, 35J65, 35Q35
Keywords: unique continuation, vortices, Ginzburg-Landau equation 
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     author = {Kukavica, Igor},
     title = {Quantitative, uniqueness, and vortex degree estimates for solutions of the {Ginzburg-Landau} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a159/}
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Kukavica, Igor. Quantitative, uniqueness, and vortex degree estimates for solutions of the Ginzburg-Landau equation. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a159/