相关论文: Unique continuation estimates for Baouendi--Grushi…
We discuss properties of $L^2$-eigenfunctions of Schr\"odinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce…
In this paper we study unique continuation theorems for magnetic Schr\"odinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimates. We consider electric and magnetic potentials with…
We consider semidiscrete finite differences schemes for the periodic Scr\"odinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bourgain in the continuous case are satisfied at the…
The goal of this paper is to analyze the pointwise controllability properties of a one-dimensional degenerate/singular equation. We prove the conditions that characterize approximate and null controllability. Besides, a numerical simulation…
We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder, and prove estimates of the…
In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator…
We characterize the absolutely continuous spectrum of half-line one-dimensional Schr\"odinger operators in terms of the limiting behavior of the Crystaline Landauer-B\"uttiker conductance of the associated finite samples.
In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equation \begin{equation*} \Delta^2_{X}u=Vu, \end{equation*} where $\Delta_{X}=\Delta_{x}+|x|^{2\alpha}\Delta_{y}$…
We obtain unique continuation results for Schrodinger equations with time dependent gradient vector potentials. This result with an appropriate modification also yields unique continuation properties for solutions of certain nonlinear…
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the class of metrics yielding an infinite deficiency…
We demonstrate a quantitative version of the usual properties related to unique continuation from an interior datum for the Schr\"odinger equation with bounded or unbounded potential. The inequalities we establish have constants that…
We prove a unique continuation principle for spectral projections of Schr\" odinger operators. We consider a Schr\" odinger operator $H= -\Delta + V$ on $\mathrm{L}^2(\mathbb{R}^d)$, and let $H_{\Lambda}$ denote its restriction to a finite…
We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been…
We investigate spectral properties of limit-periodic Schr\"odinger operators in $\ell^2(\Z)$. Our goal is to exhibit as rich a spectral picture as possible. We regard limit-periodic potentials as generated by continuous sampling along the…
In this paper, we establish unique continuation inequalities at two time points for the Dunkl--Schr\"odinger equation. The proof is based on quantitative uncertainty principles for the Dunkl transform. In particular, we prove that pairs of…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded…
We study linear co-cycles in GL(d,R) (or C) depending on a parameter (in a Lipschitz or Holder fashion) and establish Holder regularity of the Lyapunov exponents for the shift dynamics on the base. We also obtain rates of convergence of the…
We study how maximal regularity estimates with respect to the continuous functions improve automatically in cases where the spatial norm is fundamentally different from the supremum norm. More precisely, we invoke properties such as weak…
We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be $C^2$ and asymptotically periodic along the unbounded direction, with an…