MINIMIZER OF GINZBURG-LANDAU ENERGY ON THE EXTERIOR OF A BALL IN DIMENSION 3 : EXISTENCE, UNIQUENESS AND PROPERTIES
Ramona Anton · HAL (Le Centre pour la Communication Scientifique Directe) · 2020
We prove existence and unconditional uniqueness of a positive minimizer for the Ginzburg-Landau energy outside the unit ball in R 3 , satisfying Dirichlet boundary conditions. The main ingredient of the proof is a Sturm-Liouville theorem. Due to the structure of the energy space in dimension three, we obtain a strong stability of the minimizer.