Zobrazeno 1 - 10
of 208
pro vyhledávání: '"A, Léautaud"'
We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open set in a con
Externí odkaz:
http://arxiv.org/abs/2401.14820
Autor:
Léautaud, Matthieu
We consider the damped wave equation on a compact manifold. We propose different ways of measuring decay of the energy (time averages of lower energy levels, decay for frequency localized data...) and exhibit links with resolvent estimates on the ima
Externí odkaz:
http://arxiv.org/abs/2309.12709
Autor:
Laurent, Camille, Léautaud, Matthieu
These notes are intended as an introduction to the question of unique continuation for the wave operator, and some of its applications. The general question is whether a solution to a wave equation in a domain, vanishing on a subdomain has to vanish
Externí odkaz:
http://arxiv.org/abs/2307.02155
This note presents some of the results obtained in arXiv:2207.05410 and it has beenthe object of a talk of the second author during the Journ\'ees "\'Equations auxD\'eriv\'ees Partielles" (Obernai, june 2022). We study properties of geodesics that ar
Externí odkaz:
http://arxiv.org/abs/2302.04512
Autor:
Helffer, Bernard, Léautaud, Matthieu
We discuss spectral properties of the family of quartic oscillators $\mathfrak h_{\mathcal M}(\alpha) =-\frac{d^2}{dt^2} +\Big(\frac{1}{2} t^{2} -\alpha\Big)^2$ on the real line, where $\alpha\in \mathbb{R}$ is a parameter. This operator appears in a
Externí odkaz:
http://arxiv.org/abs/2209.13923
Publikováno v:
Cambridge Journal of Mathematics, 2023, 11 (4), pp.917-1043
In analogy with the study of Pollicott-Ruelle resonances on negatively curved manifolds, we define anisotropic Sobolev spaces that are well-adapted to the analysis of the geodesic vector field associated with any translation invariant Finsler metric
Externí odkaz:
http://arxiv.org/abs/2207.05410
In this article, we investigate spectral properties of the sublaplacian $-\Delta_{G}$ on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approach to the Fourier analysis on the Engel group in terms of a freque
Externí odkaz:
http://arxiv.org/abs/2206.10396
Autor:
Laurent, Camille, Léautaud, Matthieu
Publikováno v:
Tunisian J. Math. 5 (2023) 125-170
We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both s
Externí odkaz:
http://arxiv.org/abs/2203.03271
Autor:
Laurent, Camille, Léautaud, Matthieu
We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the v
Externí odkaz:
http://arxiv.org/abs/2203.03266
Autor:
Laurent, Camille, Léautaud, Matthieu
We consider damped wave (resp. Schr{\"o}dinger and plate) equations driven by a hypoelliptic "sum of squares" operator L on a compact manifold and a damping function b(x). We assume the Chow-Rashevski-H{\"o}rmander condition at rank k (at most k Lie
Externí odkaz:
http://arxiv.org/abs/2006.05122