A Hölder stability estimate for inverse problems for the ultrahyperbolic Schrödinger equation

2019 ◽  
Vol 9 (4) ◽  
pp. 2171-2199 ◽  
Author(s):  
Fikret Gölgeleyen ◽  
Özlem Kaytmaz
Keyword(s):  
Inverse Problems ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Hölder Stability

scholarly journals Carleman estimate for the Schrödinger equation and application to magnetic inverse problems

2019 ◽  
Vol 474 (1) ◽  
pp. 116-142 ◽  
Author(s):  
Xinchi Huang ◽  
Yavar Kian ◽  
Éric Soccorsi ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problems ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Carleman Estimate

Carleman inequalities and inverse problems for the Schrödinger equation

2008 ◽  
Vol 346 (1-2) ◽  
pp. 53-58 ◽  
Author(s):  
Alberto Mercado ◽  
Axel Osses ◽  
Lionel Rosier
Keyword(s):  
Inverse Problems ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Carleman Inequalities

scholarly journals A Hölder-logarithmic stability estimate for an inverse problem in two dimensions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Matteo Santacesaria
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Two Dimensions ◽  
Positive Energy ◽  
Two Dimensional ◽  
Ill Posed ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

AbstractThe problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient

scholarly journals Recovery of transversal metric tensor in the Schrödinger equation from the Dirichlet-to-Neumann map

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mourad Bellassoued ◽  
Zouhour Rezig
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Compact Riemannian Manifold ◽  
Stability Estimate ◽  
Metric Tensor ◽  
X Ray ◽  
Ray Transform ◽  
Boundary Measurements ◽  
Dirichlet To Neumann Map ◽  
Direct Use

<p style='text-indent:20px;'>In this paper, we deal with the inverse problem of determining simple metrics on a compact Riemannian manifold from boundary measurements. We take this information in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension <inline-formula><tex-math id="M1">\begin{document}$ n\geq 2 $\end{document}</tex-math></inline-formula> that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the simple metric (up to an admissible set). We also prove a Hölder-type stability estimate by the construction of geometrical optics solutions of the Schrödinger equation and the direct use of the invertibility of the geodesical X-ray transform.</p>

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