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arXiv · 2607.04715

A logarithmic convexity approach to quantitative unique continuation for the complex Ginzburg-Landau operator

Yueliang Duan·Borui Liu·Can Zhang
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Abstract

We establish quantitative unique continuation estimates for solutions of the complex Ginzburg-Landau equation in the framework of two-sphere and one-cylinder inequalities. While prior work [Dou et al. SIAM J. Control Optim. (2023)] relied on Carleman estimates, the present study develops a novel logarithmic convexity approach to prove the quantitative unique continuation property. We derive an explicit quantitative unique continuation constant and fully characterize its dependence on the parameters.

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Yueliang Duan, Borui Liu, Can Zhang. 2026-07-06. A logarithmic convexity approach to quantitative unique continuation for the complex Ginzburg-Landau operator. https://arxiv.org/abs/2607.04715

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