Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Regularity and uniqueness results for a phase change problem in binary alloys

Abstract: An isothermal model describing the separation of the components of a binary metallic alloy is considered. A phase transition process is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e., the concentration c of the first component and the phase field φ. Existence of a solution to the related initial and boundary value problem has been proved in a former paper, where, anyway, uniqueness was obtained only in a very special case. Here some further regularity and uniqueness results are shown in a more general setting using an a priori estimates – compactness argument. A key point of the proofs is the analysis of the fine continuity properties of the inverse map of the solution-dependent elliptic operator characterizing one of the equations of the system.

On the quantitative isoperimetric inequality in the plane with the barycentric distance

Abstract: In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^2(\Omega) \leq C \delta(\Omega)$ where $\delta$ is the isoperimetric deficit and $\lambda_0$ is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio $\delta(\Omega)/\lambda_0^2(\Omega)$ in the class of compact connected sets and in the class of convex sets.

Discrete Geometry and Isotropic Surfaces

Abstract: We consider smooth isotropic immersions from the 2-dimensional torus into $R^{2n}$, for $n \geq 2$. When $n = 2$ the image of such map is an immersed Lagrangian torus of $R^4$. We prove that such isotropic immersions can be approximated by arbitrarily $C^0$-close piecewise linear isotropic maps. If $n \geq 3$ the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well. The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, we introduce a numerical flow in finite dimension, whose limit provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in $R^4$. The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie.

The optimal fourth moment theorem

Abstract: We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.

Quelques approximations du temps local brownien

Abstract: We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon)\wedge t}^+ \indi_{\{X_u \leqslant 0\}} du + \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon) \wedge t}^- \indi_{\{X_u>0\}} du$ and $\frac{4}{\epsilon}\int_0^{t} X_u^- \indi_{\{X_{(u+\epsilon) \wedge t} > 0\}} du$ converge in the ucp sense to $L_t^0$, as $\epsilon \to 0$. We show that $ \frac{1}{\epsilon}\int_0^t (\indi_{\{x