890 citations · 3.5k across the 69 of their papers we have counts for
70 papers
Singular extension of critical Sobolev mappings under an exponential weak-type estimate
Bohdan Bulanyi, Jean Van Schaftingen
Given and a compact Riemannian manifold , we construct for every map in the critical Sobolev space $W^{m/(m + 1), m + 1} (\mathb…
Endpoint Sobolev inequalities for vector fields and cancelling operators
Jean Van Schaftingen
The injectively elliptic vector differential operators from to on such that the estimate \[ \Vert D^\ell u\Vert_{L^{n/(n - \ell)} (\mathbb{R…
Limiting Sobolev estimates for vector fields and cancelling differential operators
Jean Van Schaftingen
These notes present Sobolev-Gagliardo-Nirenberg endpoint estimates for classes of homogeneous vector differential operators. Away of the endpoint cases, the classical Calderón-Zygm…
Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields
Jean Van Schaftingen
Although Ornstein's nonestimate entails the impossibility to control in general all the -norm of derivatives of a function by the -norm of a constant coefficient homogene…
Lifting of fractional Sobolev mappings to noncompact covering space
Jean Van Schaftingen
Given compact Riemannian manifolds and , a Riemannian covering by a noncompact covering space $\smas…
Asymptotic behavior of minimizing -harmonic maps when in dimension 2
Jean Van Schaftingen, Benoît Van Vaerenbergh
We study --harmonic maps with Dirichlet boundary conditions from a planar domain into a general compact Riemannian manifold. We show that as approaches from below, they…
Boundary ellipticity and limiting -estimates on halfspaces
Franz Gmeineder, Bogdan Raiţă, Jean Van Schaftingen
We identify necessary and sufficient conditions on th order differential operators in terms of a fixed halfspace such that the Gagliardo--N…
Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation
Jean Van Schaftingen
We prove Gagliardo-Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and a Sobolev semi-norm, with some of th…
Spaces of Besov-Sobolev type and a problem on nonlinear approximation
Óscar Domínguez, Andreas Seeger, Brian Street +2
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space . The resulting spaces are identifie…
Reverse superposition estimates in Sobolev spaces
Jean Van Schaftingen
We study when and how the norm of a function in the homogeneous Sobolev spaces , with and either or , is…
Trace theory for Sobolev mappings into a manifold
Petru Mironescu, Jean Van Schaftingen
We review the current state of the art concerning the characterization of traces of the spaces of Sobolev mappings with value…
Lifting in compact covering spaces for fractional Sobolev mappings
Petru Mironescu, Jean Van Schaftingen
Let be a Riemannian covering, with , smooth compact connected Riemannian manifolds. If $\mathcal…
Estimates of the amplitude of holonomies by the curvature of a connection on a bundle
Sagun Chanillo, Jean Van Schaftingen
We show how the amplitude of holonomies on a vector bundle can be controlled by the integral of the curvature of the connection on a surface enclosed by the curve.
Characterization of the traces on the boundary of functions in magnetic Sobolev spaces
Hoai-Minh Nguyen, Jean Van Schaftingen
We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field is differentiable and its exterior deriva…
An estimate of the Hopf degree of fractional Sobolev mappings
Armin Schikorra, Jean Van Schaftingen
We estimate the Hopf degree for smooth maps from to in the fractional Sobolev space. Namely we show that for …
Range convergence monotonicity for vector measures and range monotonicity of the mass
Justin Dekeyser, Jean Van Schaftingen
We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict conver…
Metric characterization of the sum of fractional Sobolev spaces
Rémy Rodiac, Jean Van Schaftingen
We introduce a non-linear criterion which allows us to determine when a function can be written as a sum of functions belonging to homogeneous fractional spaces: for $\ell \in \mat…
On limiting trace inequalities for vectorial differential operators
Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen
We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},dμ)} \leq c \|μ\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\ma…
Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps
Jean Van Schaftingen
A free homotopy decomposition of any continuous map from a compact Riemmanian manifold to a compact Riemannian manifold into a finite number maps belong…
Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma
Daniel Spector, Jean Van Schaftingen
We prove a family of Sobolev inequalities of the form where $A (D) : C^\i…
Representing three-dimensional cross fields using 4th order tensors
Alexandre Chemin, François Henrotte, Jean-François Remacle +1
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in . The algebraic…
Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent
Jean Van Schaftingen, Jiankang Xia
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -Δu+ u=\big(I_α*|u|^{\fracα{N}+1}\big)|…
Groundstates of the Choquard equations with a sign-changing self-interaction potential
Luca Battaglia, Jean Van Schaftingen
We consider a nonlinear Choquard equation when the self-interaction potential is unbounded from below. Under…
Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent
Daniele Cassani, Jean Van Schaftingen, Jianjun Zhang
For the Choquard equation, which is a nonlocal nonlinear Schrödinger type equation, , in where $N\g…