Explicit expression of the microscopic renormalized energy for a pinned Ginzburg-Landau functional

Mickael dos Santos (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We get a new expression of the microscopic renormalized energy for a pinned Ginzburg-Landau type energy modeling small impurities. This is done by obtaining a sharp decomposition for the minimal energy of a Dirichlet type functional with an L ∞-weight. In particular we get an explicit expression of the microscopic renormalized energy for a circular impurity. We proceed also to the minimization of this renormalized energy in some cases.

Mots clés: Ginzburg-Landau type energy; pinning; renormalized energy Mathematics Subject Classification

Domaines: Equations aux dérivées partielles [math.AP]

Mickael dos Santos. Explicit expression of the microscopic renormalized energy for a pinned Ginzburg-Landau functional. 2018. ⟨hal-01684216v1⟩