Zobrazeno 1 - 10
of 350
pro vyhledávání: '"VAN SCHAFTINGEN, JEAN"'
Autor:
Van Schaftingen, Jean
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G6, Pp 1041-1049 (2023)
We prove Gagliardo–Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and of a Sobolev semi-norm, with some of the Sobolev semi-norms having fractional order.
Externí odkaz:
https://doaj.org/article/b663e4403cf04aa8a5537cc0baeb466d
We give sharp conditions for the limiting Korn-Maxwell-Sobolev inequalities \begin{align*} \lVert P\rVert_{{\dot{W}}{^{k-1,\frac{n}{n-1}}}(\mathbb{R}^n)}\le c\big(\lVert\mathscr{A}[P]\rVert_{{\dot{W}}{^{k-1,\frac{n}{n-1}}}(\mathbb{R}^n)}+\lVert\mathb
Externí odkaz:
http://arxiv.org/abs/2405.10349
Autor:
Van Schaftingen, Jean
The compact Riemannian manifolds $\mathcal{M}$ and $\mathcal{N}$ for which the trace operator from the first-order Sobolev space of mappings $\smash{\dot{W}}^{1, p} (\mathcal{M}, \mathcal{N})$ to the fractional Sobolev-Slobodecki\u{\i} space $\smash{
Externí odkaz:
http://arxiv.org/abs/2403.18738
We study the limiting behavior of minimizing $p$-harmonic maps from a bounded Lipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connected Riemannian manifold without boundary and with finite fundamental group as $p \nearrow 2$. We prove t
Externí odkaz:
http://arxiv.org/abs/2401.03583
Autor:
Bulanyi, Bohdan, Van Schaftingen, Jean
Publikováno v:
J. Funct. Anal. 288 (2025), n{\deg}1, 110681
Given $m \in \mathbb{N} \setminus \{0\}$ and a compact Riemannian manifold $\mathcal{N}$, we construct for every map $u$ in the critical Sobolev space $W^{m/(m + 1), m + 1} (\mathbb{S}^m, \mathcal{N})$, a map $U : \mathbb{B}^{m + 1} \to \mathcal{N}$
Externí odkaz:
http://arxiv.org/abs/2309.12874
Autor:
Van Schaftingen, Jean
The injectively elliptic vector differential operators $A (\mathrm{D})$ from $V$ to $E$ on $\mathbb{R}^n$ such that the estimate \[ \Vert D^\ell u\Vert_{L^{n/(n - \ell)} (\mathbb{R}^n)} \le \Vert A (\mathrm{D}) u\Vert_{L^1 (\mathbb{R}^n)} \] holds ca
Externí odkaz:
http://arxiv.org/abs/2305.00840
Autor:
Van Schaftingen, Jean
These notes present Sobolev-Gagliardo-Nirenberg endpoint estimates for classes of homogeneous vector differential operators. Away of the endpoint cases, the classical Calder\'on-Zygmund estimates show that the ellipticity is necessary and sufficient
Externí odkaz:
http://arxiv.org/abs/2304.14112
Autor:
Van Schaftingen, Jean
Although Ornstein's nonestimate entails the impossibility to control in general all the $L^1$-norm of derivatives of a function by the $L^1$-norm of a constant coefficient homogeneous vector differential operator, the corresponding endpoint Sobolev i
Externí odkaz:
http://arxiv.org/abs/2302.01201
Autor:
Van Schaftingen, Jean
Given compact Riemannian manifolds $\mathcal{M}$ and $\mathcal{N}$, a Riemannian covering $\pi : \smash{\widetilde{\mathcal{N}}} \to \mathcal{N}$ by a noncompact covering space $\smash{\widetilde{\mathcal{N}}}$, $1 < p < \infty$ and $0 < s < 1$, the
Externí odkaz:
http://arxiv.org/abs/2301.07663
We study $p$--harmonic maps with Dirichlet boundary conditions from a planar domain into a general compact Riemannian manifold. We show that as $p$ approaches $2$ from below, they converge up to a subsequence to a minimizing singular renormalizable h
Externí odkaz:
http://arxiv.org/abs/2301.06955