Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Lamy, Xavier"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G3, Pp 599-608 (2023)
We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with
Externí odkaz:
https://doaj.org/article/a370e13c0b7247d3b991853df680ba5d
We consider entire solutions $\omega\in\dot H^1(\mathbb R^2;\mathbb R^3)$ of the $H$-system $\Delta\omega=2\omega_x\wedge\omega_y,$ which we refer to as bubbles. Surprisingly, and contrary to conjectures raised in the literature, we find that bubbles
Externí odkaz:
http://arxiv.org/abs/2409.18068
Autor:
Lacombe, Thibault, Lamy, Xavier
We show that Lipschitz solutions $u$ of $\mathrm{div}\, G(\nabla u)=0$ in $B_1\subset\mathbb R^2$ are $C^1$, for strictly monotone vector fields $G\in C^0(\mathbb R^2;\mathbb R^2)$ satisfying a mild ellipticity condition. If $G=\nabla F$ for a strict
Externí odkaz:
http://arxiv.org/abs/2407.00775
We study differential inclusions $Du\in \Pi$ in an open set $\Omega\subset\mathbb R^2$, where $\Pi\subset \mathbb R^{2\times 2}$ is a compact connected $C^2$ curve without rank-one connections, but non-elliptic: tangent lines to $\Pi$ may have rank-o
Externí odkaz:
http://arxiv.org/abs/2404.02121
In any dimension $n\geq 3$, we prove an optimal stability estimate for the M\"obius group among maps $u\colon \mathbb S^{n-1} \to \mathbb R^n$, of the form $\inf_{\lambda>0,\phi\in \mathrm{M\"ob}(\mathbb S^{n-1})} \int_{\mathbb S^{n-1}}\left|\frac 1\
Externí odkaz:
http://arxiv.org/abs/2401.06593
Autor:
Contreras, Andres, Lamy, Xavier
In a two dimensional annulus $A_\rho=\{x\in \mathbb R^2: \rho<|x|<1\}$, $\rho\in (0,1)$, we characterize $0$-homogeneous minimizers, in $H^1(A_\rho;\mathbb S^1)$ with respect to their own boundary conditions, of the anisotropic energy \begin{equation
Externí odkaz:
http://arxiv.org/abs/2311.15758
In this work we prove a sharp quantitative form of Liouville's theorem, which asserts that, for all $n\geq 3$, the weakly conformal maps of $\mathbb S^{n-1}$ with degree $\pm 1$ are M\"obius transformations. In the case $n=3$ this estimate was first
Externí odkaz:
http://arxiv.org/abs/2305.19886
Autor:
Kowalczyk, Michał, Lamy, Xavier
We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus, starting from an initial data with a finite number of nondegenerate zeros -- but possibly very high initial energy. We show that the initial zeros are conserved and the flow
Externí odkaz:
http://arxiv.org/abs/2211.15773
Autor:
Lamy, Xavier, Marconi, Elio
We consider entropy solutions to the eikonal equation $|\nabla u|=1$ in two space dimensions. These solutions are motivated by a class of variational problems and fail in general to have bounded variation. Nevertheless they share with BV functions, s
Externí odkaz:
http://arxiv.org/abs/2211.11522
Autor:
Lamy, Xavier, Marconi, Elio
We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vo
Externí odkaz:
http://arxiv.org/abs/2209.09662