Related papers: Uniqueness Properties for Discrete equations and C…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
A degenerate Schr\"{o}dinger equation under fractional integral damping is considered. Here the damping term is singular and not integrable and we consider the two cases when damping acting on the degenerate boundary and nondegenerate…
In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. As applications of these discrete Carleman estimates, we apply them to study two inverse problems…
In this paper we analyze the dispersion property of some models involving Schr\"odinger equations. First we focus on the discrete case and then we present some results on graphs.
We prove that the material parameters in a Dirac system with magnetic and electric potentials are uniquely determined by measurements made on a possibly small subset of the boundary. The proof is based on a combination of Carleman estimates…
Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schr\"odinger operators are extended to allow singular potentials such as certain $L^p$-functions. The proof is based on accordingly adapted Carleman…
In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e., noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in…
We study the quantitative unique continuation on the boundary for solutions of elliptic equations with Neumann boundary conditions for bounded potentials and boundary potentials on compact manifolds with boundary. The boundary doubling…
We prove unique continuation properties for linear variable coefficient Schr\"odinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any…
We discuss the application of the Discrete Variable Representation to Schr\"odinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost…
A Carleman estimate and the unique continuation of solutions for an anomalous diffusion equation with fractional time derivative of order $0<\alpha<1$ are given. The estimate is derived via some subelliptic estimate for an operator…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
In this paper, we establish a quantitative weak unique continuation theorem on an annular domain for a backward degenerate parabolic equation with a degenerate interior point. Our methodology hinges on approximating the solution of the…
We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the boundary of the domain. These estimates are…
In this article, we study the quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms. We quantify the strong unique continuation property by estimating the maximal vanishing order of…
Bounded variation estimates of Galerkin approximations are established in order to extract an almost everywhere convergent subsequence of Galerkin approximations. As a result we prove existence of weak solutions of initial boundary value…
We prove a family of identities that involve the solutions to the free Schreodinger equation. As a consequence of these identities we shall deduce a lower bound for the local smoothing estimate and a uniqueness criterion.
In this article, we focus on the analysis of discrete versions of the Calderon problem in dimension d \geq 3. In particular, our goal is to obtain stability estimates for the discrete Calderon problems that hold uniformly with respect to…
Via Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditions. The additional information supplied prescribes the…
In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…