95 citations · 342 across the 18 of their papers we have counts for
18 papers
Stationary -harmonic maps approaching planar singular harmonic maps to the circle
Marco Badran, Jean Van Schaftingen
Given a bounded planar domain , we show that any singular harmonic map into the circle corresponding to a topologically nondegenerate critical…
Trace theory for gauge-covariant Sobolev spaces
Jean Van Schaftingen, Leon Winter
The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle for some connection are characterised as some gauge-covariant fractional Sobolev spaces when the curvatur…
The extension of traces for Sobolev mappings between manifolds
Jean Van Schaftingen
The compact Riemannian manifolds and for which the trace operator from the first-order Sobolev space of mappings $\smash{\dot{W}}^{1, p} (\mathcal{M}, \…
Limiting behavior of minimizing -harmonic maps in 3d as goes to with finite fundamental group
Bohdan Bulanyi, Jean Van Schaftingen, Benoît Van Vaerenbergh
We study the limiting behavior of minimizing -harmonic maps from a bounded Lipschitz domain to a compact connected Riemannian manifold without boundary…
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail
Haïm Brezis, Jean Van Schaftingen, Po-Lam Yung
In the cases where there is no Sobolev-type or Gagliardo-Nirenberg-type fractional estimate involving , we establish alternative estimates where the stron…
Quantitative characterization of traces of Sobolev maps
Katarzyna Mazowiecka, Jean Van Schaftingen
We give a quantitative characterization of traces on the boundary of Sobolev maps in , where and are compact Riem…
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…
Vortex motion for the lake equations
Justin Dekeyser, Jean Van Schaftingen
The lake equations $$\left\{\begin{aligned} \nabla \cdot \big( b \, \mathbf{u}\big) &= 0 & & \text{on}\ \mathbb{R}\times D,\\ \partial_t\mathbf{u} + (\mathbf{u}\cdot \nabla)\mathbf…
Higher order weak differentiability and Sobolev spaces between manifolds
Alexandra Convent, Jean Van Schaftingen
We define the notion of higher-order colocally weakly differentiable maps from a manifold to a manifold . When and are endowed with Riemannian metrics, and…
Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem
Sagun Chanillo, Jean Van Schaftingen, Po-Lam Yung
We offer a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on . We use this idea to extend the result to real hyperbolic spaces $\mathbb{…
Existence of groundstates for a class of nonlinear Choquard equations in the plane
Luca Battaglia, Jean Van Schaftingen
We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation where is the…
Groundstates and radial solutions to nonlinear Schrödinger-Poisson-Slater equations at the critical frequency
Carlo Mercuri, Vitaly Moroz, Jean Van Schaftingen
We study the nonlocal Schrödinger-Poisson-Slater type equation where , ,…
Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field
Jonathan Di Cosmo, Jean Van Schaftingen
We construct solutions to the nonlinear magnetic Schrödinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 Δ_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\…
Desingularization of vortex rings and shallow water vortices by semilinear elliptic problem
Sébastien de Valeriola, Jean Van Schaftingen
Steady vortices for the three-dimensional Euler equation for inviscid incompressible flows and for the shallow water equation are constructed and showed to tend asymptotically to s…
Limiting fractional and Lorentz spaces estimates of differential forms
Jean Van Schaftingen
We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R^n in terms of their L^1 norm.