78 citations · 84 across the 5 of their papers we have counts for
7 papers · 1 filter
Renormalised energy between boundary vortices in thin-film micromagnetics with Dzyaloshinskii-Moriya interaction
Radu Ignat, François L'Official
We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reducti…
Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension
Radu Ignat, Mickael Nahon, Luc Nguyen
We prove that the degree-one vortex solution is the unique minimizer for the Ginzburg--Landau functional for gradient fields (that is, the Aviles--Giga model) in the unit ball $B^N…
Vortex sheet solutions for the Ginzburg-Landau system in cylinders: symmetry and global minimality
Radu Ignat, Mircea Rus
We consider the Ginzburg-Landau energy for -valued maps defined in a cylinder shape domain satisfying a degree-one vortex boundary condition…
A regularizing property of the -eikonal equation
Camillo De Lellis, Radu Ignat
We prove that any -dimensional solution of the eikonal equation has locally Lipschitz gradient except at a locally finite number of vo…
A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls
Raphael Cote, Radu Ignat, Evelyne Miot
We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers (Néel walls). We first establish compactness of…
Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (so called "melting hedgehog") in the framework of the Landau - de Gennes…