Uniqueness of minimisers of Ginzburg-Landau functionals – Luc Nguyen

By | May 4, 2018

We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\RR^n$-valued maps under suitable convexity assumption on the potential and for $H^{1/2} \cap L^\infty$ boundary data that is non-negative in a fixed direction $e\in \SSphere^{n-1}$. Furthermore, we show that, when minimisers are non-unique, the set of minimisers is invariant under appropriate orthogonal transformations of $\RR^n$. As an application, we obtain symmetry results for minimisers corresponding to symmetric Dirichlet boundary data. We also prove corresponding results for harmonic maps. Joint work with R. Ignat, V. Slastikov and A. Zarnescu.