MINIMIZER OF GINZBURG-LANDAU ENERGY ON THE EXTERIOR OF A BALL IN DIMENSION 3 : EXISTENCE, UNIQUENESS AND PROPERTIES

Ramona Anton (1, 2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 SU - Sorbonne Université

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.

Domaines: Mathématiques [math]

Ramona Anton. MINIMIZER OF GINZBURG-LANDAU ENERGY ON THE EXTERIOR OF A BALL IN DIMENSION 3 : EXISTENCE, UNIQUENESS AND PROPERTIES. 2020. ⟨hal-02969436⟩