# Global uniform estimate for the modulus of 2D Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy

Abstract : For $\varepsilon>0$, let $u_\varepsilon:\Omega\to \mathbb R^2$ be a solution of the Ginzburg-Landau system $-\Delta u_\varepsilon=\frac 1{\varepsilon^2} u_\varepsilon (1-|u_\varepsilon|^2)$ in a Lipschitz bounded domain $\Omega$. In an energy regime that excludes interior vortices, we prove that $1-|u_\varepsilon|$ is uniformly estimated by a positive power of $\varepsilon$ $globally$ in $\Omega$ provided that the energy of $u_\varepsilon$ at the boundary $\partial \Omega$ does not grow faster than $\varepsilon^{-\alpha}$ with $\alpha\in (0,1)$.
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https://hal.archives-ouvertes.fr/hal-02265220
Submitted on : Thursday, August 8, 2019 - 6:55:48 PM
Last modification on : Monday, August 19, 2019 - 1:45:57 PM

### Identifiers

• HAL Id : hal-02265220, version 1
• ARXIV : 1904.00856

### Citation

Radu Ignat, Matthias Kurzke, Xavier Lamy. Global uniform estimate for the modulus of 2D Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy. 2019. ⟨hal-02265220⟩

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