Results 1 to 10 of about 3,278,872 (203)

Unique continuation for the magnetic Schrödinger equation. [PDF]

Int J Quantum Chem, 2020
AbstractThe unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is identically zero.
Laestadius A, Benedicks M, Penz M.
europepmc   +8 more sources

Quantitative unique continuation for the linear coupled heat equations [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of R d $\mathbb{R}^{d}$ with smooth boundary ∂Ω.
Guojie Zheng, Keqiang Li, Jun Li
doaj   +2 more sources

Quantitative unique continuation for the heat equations with inverse square potential [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of Rd $\mathbb{R}^{d}$. We establish observation estimates for solutions of equations.
Guojie Zheng, Keqiang Li, Yuanyuan Zhang
doaj   +2 more sources

Optimal Approximation of Unique Continuation

Foundations of Computational Mathematics
We consider numerical approximations of ill-posed elliptic problems with conditional stability. The notion of optimal error estimates is defined including both convergence with respect to discretisation and perturbations in data.
Erik Burman, Mihai Nechita, L. Oksanen
semanticscholar   +5 more sources

Unique Continuation for the Momentum Ray Transform

Journal of Fourier Analysis and Applications, 2023
The present article focuses on a unique continuation result for certain weighted ray transforms, utilizing the unique continuation property (UCP) of the fractional Laplace operator.
Joonas Ilmavirta, Pu-Zhao Kow, S. K. Sahoo   +2 more
semanticscholar   +4 more sources

Unique continuation theorems for biharmonic maps. [PDF]

Bull Lond Math Soc, 2019
We prove several unique continuation results for biharmonic maps between Riemannian manifolds.
Branding V, Oniciuc C.
europepmc   +7 more sources

Unique continuation on planar graphs

Discrete Analysis
Unique continuation on planar graphs, Discrete Analysis 2025:16, 12 pp. A fundamental result in harmonic analysis is Liouville's theorem for harmonic functions: that a bounded harmonic function on $\mathbb R^n$ is constant.
Ahmed Bou-Rabee, William Cooperman, Shirshendu Ganguly   +2 more
doaj   +4 more sources

On Unique Continuation for Navier-Stokes Equations [PDF]

Abstract and Applied Analysis, 2015
We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable ...
Zhiwen Duan, Shuxia Han, Peipei Sun
doaj   +4 more sources

Unique continuation for a mean field game system [PDF]

Applied Mathematics Letters, 2023
For a mean field game system, we prove the unique continuation which asserts that if Cauchy data are zero on arbitrarily chosen lateral subboundary, then the solution identically vanishes.
O. Imanuvilov, Hongyu Liu, Masahiro Yamamoto   +2 more
semanticscholar   +1 more source

Strong Unique Continuation from the Boundary for the Spectral Fractional Laplacian [PDF]

E S A I M: Control, Optimisation and Calculus of Variations, 2023
We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian.
Alessandra De Luca, V. Felli, Giovanni Siclari   +2 more
semanticscholar   +1 more source