相关论文: Unique continuation for the Schrodinger equation w…
We prove unique continuation properties related to the Hardy uncertainty principle for solutions of the hyperbolic nonlinear Schr\"odinger equation and the hyperbolic Schr\"odinger equation with potential. Under suitable conditions on the…
This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori…
We investigate the solutions for a time dependent potential by considering two scenarios for the fractional Schr\"odinger equation. The first scenario analyzes the influence of the time dependent potential in the absence of the kinetic…
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and…
We study quantitative unique continuation for second order elliptic equations with lower-order terms of H\"older regularity via a weighted frequency function method. We establish quantitative three-ball inequalities and corresponding…
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our…
In this paper, we present several observability and unique continuation inequalities for the free Schr\"{o}dinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in…
We prove a quantitative unique continuation principle for Schr\"odinger operators $H=-\Delta+V$ on $\mathrm{L}^2(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^d$ and $V$ is a singular potential: $V \in \mathrm{L}^\infty(\Omega)…
We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable…
We utilize the theory of de Branges spaces to show when certain Schr\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness…
We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…
In this article we prove the property of unique continuation (also known for C^\infty functions as quasianalyticity) for solutions of the differential inequality |\Delta u| \leq |Vu| for V from a wide class of potentials (including…
We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…
English version of the abstract. We study path-wise uniqueness property of a class of stochastic differential equations with local time and sojourn time in the boundary. ----- French version of the abstract. Nous \'etudions l'unicit\'e…
We investigate the uniqueness, in suitable weighted $\ell^p$ spaces, of solutions to the Schr\"odinger equation with a potential, posed on infinite graphs. The potential can tend to zero at infinite with a certain rate.
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
We consider the relativistic Schr\"odinger (Gordon-Klein) equation with a time dependent vector and a scalar potential on a bounded cylindrical domain. Using a standard Geometric Optics Ansatz, we establish a logarithmic stability estimate…
We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…
The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time.…