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We consider complex-valued solutions $u_{ε}$ of the Ginzburg–Landau equation on a smooth bounded simply connected domain $Ω$ of $ℝ^{N}$ , $N \geq 2$ , where $ε > 0$ is a small parameter. We assume that the Ginzburg–Landau energy $E_{ε} (u_{ε})$ verifies the bound (natural in the context) $E_{ε} (u_{ε}) \leq M_{0} | log ε |$ , where $M_{0}$ is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of $u_{ε}$ , as $ε \to 0$ , is to establish uniform $L^{p}$ bounds for the gradient, for some $p > 1$ . We review some recent techniques developed in...

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of $ℝ^{N}$ , N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy $E_{ε} (u_{ε})$ verifies the bound (natural in the context) $E_{ε} (u_{ε}) \leq M_{0} | log ε |$ , where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...

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Über die endliche Lösbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten.

Über die Stetigkeit teilweise freier Minimalflächen.

Über einfache Mannigfaltigkeiten im linearen affinen Raum $A_{n}$ in globaler Auffassung

Über Stabilität und Isoliertheit der Lösungen des Klassischen Plateauproblems.

Un problème spectral inverse sur les surfaces

Une preuve probabiliste élémentaire d'un résultat de P. Baird et J. C. Wood

Une théorie de Morse pour les systèmes hamiltoniens convexes

Uniform estimates for the parabolic Ginzburg–Landau equation

Uniform estimates for the parabolic Ginzburg–Landau equation

Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions.

Uniqueness for the harmonic map flow from surface to general targets.

Uniqueness of Harmonie Mappings and of Solutions of Elliptic Equations on Riemannnian Manifolds.

Unitons and their moduli.

Unstable Solutions of the Euler Equations of Certain Variational Problems.

Upper bound for the number of eigenvalues for nonlinear operators

Upper critical field and location of surface nucleation of superconductivity

Currently displaying 1 – 16 of 16