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Bibliographic Details
Main Authors: Bronsard, Lia, Colinet, Andrew, Stantejsky, Dominik
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.09949
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Table of Contents:
  • We consider minimizers $u_\varepsilon$ 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 $L^\infty$-bound uniform in $\varepsilon$ when $Ω$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\varepsilon^{-1}$ when $Ω$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition.