95 citations · 342 across the 18 of their papers we have counts for
4 papers · 1 filter
Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold
Antonin Monteil, Rémy Rodiac, Jean Van Schaftingen
We study the asymptotic behaviour, as a small parameter tends to zero, of minimisers of a Ginzburg-Landau type energy with a nonlinear penalisation potential vanishin…
Limiting Sobolev and Hardy inequalities on stratified homogeneous groups
Jean Van Schaftingen, Po-Lam Yung
We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known canc…
Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains
Antonin Monteil, Rémy Rodiac, Jean Van Schaftingen
We define renormalised energies for maps that describe the first-order asymptotics of harmonic maps outside of singularities arising due to obstructions generated by the boundary d…
A surprising formula for Sobolev norms
Haim Brezis, Jean Van Schaftingen, Po-Lam Yung
We establish the equivalence between the Sobolev semi-norm and a quantity obtained when replacing the strong by a weak norm in the Gagliardo semi-n…