Related papers: A lower bound for the principal eigenvalue of the …

Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality and $H^1$ conformity of the velocity field. Most previous…

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving…

Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many…

Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively…

Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma:={\mathbb E}(X\otimes X).$ Let $\Sigma=\sum_{r\geq 1}\mu_r P_r$ be the spectral decomposition of $\Sigma$ with…

In the limit $\hbar\to 0$, we analyze a class of Schr\"odinger operators $H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a vector bundle $\mathcal{Eh}$ over a Riemannian manifold $M$ where $L$ is a Laplace type…

This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming…

We derive a sharp bound on the location of non-positive eigenvalues of Schroedinger operators on the halfline with complex-valued potentials.

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…

We prove a quantum ergodicity theorem in position space for the eigenfunctions of a Schr\"odinger operator $-\Delta+V$ on a rectangular torus $\mathbb{T}^2$ for $V\in L^2(\mathbb{T}^2)$ with an algebraic rate of convergence in terms of the…

We investigate $L^1(\mathbb R^n)\to L^\infty(\mathbb R^n)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there is an eigenvalue at zero energy and $n\geq 5$ is odd. In particular, we show that if there is an…

The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…

We investigate the Stark operator restricted to a bounded domain $\Omega\subset\mathbb{R}^2$ with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been…

We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, exhibit both dynamical localization and…

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…

In this paper a description of the small-$\hbar$ limit of loci of zeros of fundamental solutions for polynomial potentials is given. The considered cases of the potentials are bounded to the ones which provided us with simple turning points…

We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…

We relate the existence and regularity of a solution operator to on smoothly bounded pseudoconvex domains to the existence and regularity of a projection operator onto the kernel of dbar.

For a large class of semiclassical pseudodifferential operators, including Schr\"odinger operators, $ P (h) = -h^2 \Delta_g + V (x) $, on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside…