4 papers
On Aviles-Giga limit states with entropy productions
Xavier Lamy, Andrew Lorent, Guanying Peng
The Aviles-Giga energy provides sequences of maps converging to weak solutions of the eikonal equation \begin{align*} \mathrm{div}\, m=0…
Hyperbolic regularization effects for degenerate elliptic equations
Xavier Lamy, Riccardo Tione
This paper investigates the regularity of Lipschitz solutions to the general two-dimensional equation with highly degenerate ellipticity. Just assuming st…
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…
Interaction energies in nematic liquid crystal suspensions
Lia Bronsard, Xavier Lamy, Dominik Stantejsky +1
We establish, as , an asymptotic expansion for the minimal Dirichlet energy of -valued maps outside a finite number of three-dimensional particles of size $Ï…