Search results for "Père"

Convexities and optimal transport problems on the Wiener space

2013

The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dime…

Shape optimization for monge-ampére equations via domain derivative

2011

In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.

New isoperimetric estimates for solutions to Monge - Ampère equations

2009

Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.

Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator

2017

We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampere operator as well as to the second order elliptic problem which arises after an implicit time discretization of the dynamical equation. Curiously, the dynamical problem corresponds to a third order operator but becomes a singular second order parabolic equation (involving the 3-Laplacian operator) in the class of radially symmetric convex functions. Using symmetrization techniques some quantitative comparison estimates and several qualitative properties of solutions are given.

Stability of radial symmetry for a Monge-Ampère overdetermined problem

2008

Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.

A note on Sobolev isometric immersions below W2,2 regularity

2017

Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.

Quelles précautions prendre lorsqu'on enquête sur les groupes de pères ? Contraintes et ressources d'Internet et des réseaux en ligne

2016

National audience; Les terrains d'enquête sujets à controverse et dont le ou la sociologue ne se sent pas proche idéologiquement sont particulièrement difficiles à « tenir » sur plusieurs années, a fortiori depuis l'émergence de l'ère numérique. Si les chercheur-e-s sont amené-e-s - afin de légitimer leur objet de recherche, mais aussi tout simplement dans une perspective de carrière - à publier sur leur enquête alors qu'elle est en train de se faire, la porosité des frontières entre la sphère médiatique et la sphère académique, rendue possible par Internet et les moteurs de recherche, rend de plus en plus difficile la non diffusion de ses résultats de recherche auprès de ses enquêté-e-s. C…

Integrating the Kadomtsev-Petviashvili Equation in the 1+3 Dimensions VIA the Generalised Monge-Ampère Equation: An Example of Conditioned Painlevé T…

1994

Approximation by mappings with singular Hessian minors

2018

Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.

A symmetrization result for Monge–Ampère type equations

2007

In this paper we prove some comparison results for Monge–Ampere type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)