A priori L ∞ −bound for Ginzburg-Landau energy minimizers with divergence penalization
Lia Bronsard, Andrew Colinet, Dominik Stantejsky · Communications in Partial Differential Equations · 2025
.We consider minimizers uε of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain Ω. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a L∞-bound uniform in ε when Ω has 𝐶2,1−boundary and that the Lipschitz constant blows up like ε−1 when Ω has 𝐶3,1−boundary. Our theorem extends to a 𝑊2,𝑝−regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition.