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math.AP2025
Compensation effects for anisotropic energies of two-dimensional unit vector fields
Lia Bronsard, Dmitry Golovaty, Xavier Lamy +1
We study the highly anisotropic energy of two-dimensional unit vector fields given by \begin{align*} E_ε(u)= \int_Ω (\mathrm{div}\,u)^2 + ε(\mathrm{curl}\,u)^2\, dx\,, \quad u\colo…
math.AP2025
A Ginzburg-Landau problem on a circular cone
Christian Cofoid, Dmitry Golovaty, Etienne Sandier +1
We carry out an asymptotic analysis for a Ginzburg-Landau type model for tangent vector fields defined on a cone. The results, in the spirit of Brezis, Bethuel and Helein, establis…