10 papers
A priori estimates and compactness for anisotropic Ginzburg-Landau minimizers with tangential anchoring
Lia Bronsard, Andrew Colinet, Dominik Stantejsky +1
We consider minimizers of the Ginzburg-Landau energy with quadratic divergence or curl penalization on a simply-connected two-dimensional domain . On the bounda…
Minimizing solutions of degenerate Allen-Cahn equations with three wells in
Lia Bronsard, Ãtienne Sandier, Peter Sternberg
We characterize all minimizers of the vector-valued Allen-Cahn equation in under the assumption that the potential has three wells and that the associated degene…
Asymptotics for Minimizers of Landau-de Gennes with a Magnetic Field and Tangential Anchoring
Lia Bronsard, Dean Louizos, Dominik Stantejsky
In this article we prove existence of minimizers of the Landau-de Gennes energy for liquid crystals with homogeneous external magnetic field and strong uniaxial planar anchoring. N…
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\c…
On the non-uniqueness of locally minimizing clusters via singular cones
Lia Bronsard, Robin Neumayer, Michael Novack +1
We construct partitions of into three sets that locally minimize interfacial area among compactly supported volume…
An Infinite Double Bubble Theorem
Lia Bronsard, Michael Novack
The classical double bubble theorem characterizes the minimizing partitions of into three chambers, two of which have prescribed finite volume. In this paper we prov…