Énergies relaxées pour applications harmoniques
A characterization of maps in which can be approximated by smooth maps
Le problème des surfaces à courbure moyenne prescrite
Fonctionnelles de Ginzburg-Landau et espaces de configurations de particules positives et négatives
Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité
Uniform estimates for the parabolic Ginzburg–Landau equation
We consider complex-valued solutions of the Ginzburg–Landau equation on a smooth bounded simply connected domain of , , where is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of , as , is to establish uniform bounds for the gradient, for some . We review some recent techniques developed in...
Uniform estimates for the parabolic Ginzburg–Landau equation
We consider complex-valued solutions u of the Ginzburg–Landau equation on a smooth bounded simply connected domain of , ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy verifies the bound (natural in the context) , where is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u, as ε → 0, is to establish uniform bounds for the gradient, for some . We review...
Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics
We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.
On the NLS dynamics for infinite energy vortex configurations on the plane.
Page 1