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Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation

Leonid BerlyandVolodymyr Rybalko — 2010

Journal of the European Mathematical Society

We study solutions of the 2D Ginzburg–Landau equation - Δ u + ε - 2 u ( | u | 2 - 1 ) = 0 subject to “semi-stiff” boundary conditions: Dirichlet conditions for the modulus, | u | = 1 , and homogeneous Neumann conditions for the phase. The principal result of this work shows that there are stable solutions of this problem with zeros (vortices), which are located near the boundary and have bounded energy in the limit of small ε . For the Dirichlet boundary condition (“stiff” problem), the existence of stable solutions with vortices, whose energy...

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