Jean Van Schaftingen

activity

20072023

most citedGroundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics

890 citations · 3.5k across the 69 of their papers we have counts for

collaborators

Showing math.FAShow all

18 papers · 1 filter

math.FA2021★ 12 cited

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 $W ˙^{1, p}$ . The resulting spaces are identifie…

math.FA2019★ 1 cited

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 $A$ is differentiable and its exterior deriva…

math.FA2018

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 $M$ to a compact Riemannian manifold $N$ into a finite number maps belong…

math.FA2017★ 5 cited

Uniform boundedness principles for Sobolev maps into manifolds

Antonin Monteil, Jean Van Schaftingen

Given a connected Riemannian manifold $N$ , an $m$--dimensional Riemannian manifold $M$ which is either compact or the Euclidean space, $p \in [1, + \infty)$ and…

math.FA2017★ 2 cited

Weak approximation by bounded Sobolev maps with values into complete manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen

We have recently introduced the trimming property for a complete Riemannian manifold $N^{n}$ as a necessary and sufficient condition for bounded maps to be strongly dense in $W^{1,…

math.FA2016★ 44 cited

Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces

Jacopo Bellazzini, Marco Ghimenti, Carlo Mercuri +2

We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$\|φ\|_{L^p(\mathbb{R}^d)}\le C\|φ\|_{\dot H^{s}(\mathbb{R}^d)}^β \left(\iint_{\mathbb{R}^d \times \ma…

math.FA2015★ 2 cited

Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds

Mircea Petrache, Jean Van Schaftingen

Given $n \in N_{*}$ , a compact Riemannian manifold $M$ and a Sobolev map $u \in W^{n / (n + 1), n + 1} (S^{n}; M)$ , we construct a map $U$ in the Sobolev-Marcinkiewicz…

math.FA2015★ 8 cited

Density of bounded maps in Sobolev spaces into complete manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen

Given a complete noncompact Riemannian manifold $N^{n}$ , we investigate whether the set of bounded Sobolev maps $(W^{1, p} \cap L^{\infty}) (Q^{m}; N^{n})$ on the cube $Q^{m}$ is strongly de…

math.FA2014★ 35 cited

An $L^{1}$ -type estimate for Riesz potentials

Armin Schikorra, Daniel Spector, Jean Van Schaftingen

In this paper we establish new $L^{1}$ -type estimates for the classical Riesz potentials of order $α \in (0, N)$ : \[ \|I_αu\|_{L^{N/(N-α)}(\mathbb{R}^N)} \leq C \|Ru\|_{L^1(\mathbb{R}…

math.FA2014★ 1 cited

Equivalence between Polyá-Szegő and relative capacity inequalities under rearrangement

Jean Van Schaftingen

The transformations of functions acting on sublevel sets that satisfy a Pólya-Szegő inequality are characterized as those being induced by transformations of sets that do not incre…

math.FA2013★ 7 cited

Approximation in Sobolev spaces by piecewise affine interpolation

Jean Van Schaftingen

Functions in a Sobolev space are approximated directly by piecewise affine interpolation in the norm of the space. The proof is based on estimates for interpolations and does not r…

math.FA2013★ 6 cited

Intrinsic weak derivatives and Sobolev spaces between manifolds

Alexandra Convent, Jean Van Schaftingen

We define the notion of colocally weakly differentiable maps from a manifold $M$ to a manifold $N$ . If $p \geq 1$ and $M$ and $N$ are endowed with a Riemannian metric, this allows u…

math.FA2013★ 16 cited

Strong approximation of fractional Sobolev maps

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen

Brezis and Mironescu have announced several years ago that for a compact manifold $N^{n} \subset R^{ν}$ and for real numbers $0 < s < 1$ and $1 \leq p < \infty$ the class $C^\i…

math.FA2013★ 62 cited

Hardy-Sobolev inequalities for vector fields and canceling linear differential operators

Pierre Bousquet, Jean Van Schaftingen

Given a homogeneous k-th order differential operator $A (D)$ on $R^{n}$ between two finite dimensional spaces, we establish the Hardy inequality $$\int_{\mathbb{R}^n} \frac{…

math.FA2012★ 17 cited

Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ℓ$ simply connected manifolds when $s \geq 1$

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen

Given a compact manifold $N^{n} \subset R^{ν}$ , $s \geq 1$ and $1 \leq p < \infty$ , we prove that the class of smooth maps on the cube with values into $N^{n}$ is strongly dense i…

math.FA2012★ 13 cited

Strong density for higher order Sobolev spaces into compact manifolds

Pierre Bousquet, Augusto Ponce, Jean Van Schaftingen

Given a compact manifold $N^{n}$ , an integer $k \in N_{*}$ and an exponent $1 \leq p < \infty$ , we prove that the class $C^{\infty} (Q^{m}; N^{n})$ of smooth maps on the cu…

math.FA2009★ 44 cited

Explicit approximation of the symmetric rearrangement by polarizations

Jean Van Schaftingen

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial…

math.FA2009

Closure of Smooth Maps in $W^{1, p} (B^{3}; S^{2})$

Augusto C. Ponce, Jean Van Schaftingen

For every $2 < p < 3$ , we show that $u \in W^{1, p} (B^{3}; S^{2})$ can be strongly approximated by maps in $C^\infty(\Bar{B}^3; S^2)$ if, and only if, the distributional Jacobian of $u$ …

Spaces of Besov-Sobolev type and a problem on nonlinear approximation

Characterization of the traces on the boundary of functions in magnetic Sobolev spaces

Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps

Uniform boundedness principles for Sobolev maps into manifolds

Weak approximation by bounded Sobolev maps with values into complete manifolds

Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces

Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds

Density of bounded maps in Sobolev spaces into complete manifolds

An L1-type estimate for Riesz potentials

Equivalence between Polyá-Szegő and relative capacity inequalities under rearrangement

Approximation in Sobolev spaces by piecewise affine interpolation

Intrinsic weak derivatives and Sobolev spaces between manifolds

Strong approximation of fractional Sobolev maps

Hardy-Sobolev inequalities for vector fields and canceling linear differential operators

Density of smooth maps for fractional Sobolev spaces Ws,p into ℓ simply connected manifolds when s≥1

Strong density for higher order Sobolev spaces into compact manifolds

Explicit approximation of the symmetric rearrangement by polarizations

Closure of Smooth Maps in W1,p(B3;S2)

An $L^{1}$ -type estimate for Riesz potentials

Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ℓ$ simply connected manifolds when $s \geq 1$

Closure of Smooth Maps in $W^{1, p} (B^{3}; S^{2})$