# J. Schaftingen

Author pages are created from data sourced from our academic publisher partnerships and public sources.

- Publications
- Influence

Existence of groundstates for a class of nonlinear Choquard equations

- Vitaly Moroz, J. Schaftingen
- Mathematics
- 10 December 2012

We prove the existence of a nontrivial solution 𝑢 ∈ H¹ (ℝ^N) to the nonlinear Choquard equation -Δ 𝑢 + 𝑢 = (I_α * 𝐹 (𝑢)) 𝐹' (𝑢) in ℝ^N, where I_α is a Riesz potential, under almost necessary… Expand

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

- Vitaly Moroz, J. Schaftingen
- Mathematics
- 29 May 2012

We consider a semilinear elliptic problem \[ - \Delta u + u = (I_\alpha \ast \abs{u}^p) \abs{u}^{p - 2} u\quad\text{in \(\R^N\),} \] where \(I_\alpha\) is a Riesz potential and \(p>1\). This family… Expand

Semi-classical states for the Choquard equation

- Vitaly Moroz, J. Schaftingen
- Mathematics
- 7 August 2013

We study the nonlocal equation $$\begin{aligned} -\varepsilon ^2 \Delta u_\varepsilon +V u_\varepsilon = \varepsilon ^{-\alpha }\bigl (I_\alpha *|u_\varepsilon |^p\bigr ) |u_\varepsilon |^{p - 2}… Expand

Symmetrization and minimax principles

- J. Schaftingen
- Mathematics
- 1 August 2005

We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points. It… Expand

Desingularization of Vortices for the Euler Equation

- D. Smets, J. Schaftingen
- Mathematics
- 7 September 2009

We study the existence of stationary classical solutions of the incompressible Euler equation in the planes that approximate singular stationary solutions of this equation. The construction is… Expand

Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials

- Vitaly Moroz, J. Schaftingen
- Mathematics
- 4 February 2009

We study the existence of positive solutions for a class of nonlinear Schrödinger equations of the type $$-{\varepsilon}^2\Delta u + Vu = u^p\quad{{\rm in}\,{\mathbb R}^N},$$where N ≥ 3, p > 1 is… Expand

Periodic homogenization of monotone multivalued operators

- A. Damlamian, N. Meunier, J. Schaftingen
- Mathematics
- 15 December 2007

Using the unfolding method of Cioranescu, Damlamian and Griso [D. Cioranescu, A. Damlanuan, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris Math. 335 (1) (2002) 99-104], we… Expand

Subelliptic Bourgain-brezis Estimates On Groups

- S. Chanillo, J. Schaftingen
- Mathematics
- 21 December 2007

We show that divergence-free $\mathrm{L}^1$ vector fields on a nilpotent homogeneous group of homogeneous dimension $Q$ are in the dual space of functions whose gradient is in $\mathrm{L}^Q$. This… Expand

A guide to the Choquard equation

- Vitaly Moroz, J. Schaftingen
- Mathematics
- 7 June 2016

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right)… Expand

Limiting Sobolev inequalities for vector fields and canceling linear differential operators

- J. Schaftingen
- Mathematics
- 1 April 2011

The estimate \[ \norm{D^{k-1}u}_{L^{n/(n-1)}} \le \norm{A(D)u}_{L^1} \] is shown to hold if and only if \(A(D)\) is elliptic and canceling. Here \(A(D)\) is a homogeneous linear differential operator… Expand