Stability estimates for the Calder\'on problem with partial data
| Autor: | Pedro Caro, David Dos Santos Ferreira, Alberto Ruiz |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics [Helsinki], Falculty of Science [Helsinki], University of Helsinki-University of Helsinki, Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), Helsingin yliopisto = Helsingfors universitet = University of Helsinki-Helsingin yliopisto = Helsingfors universitet = University of Helsinki, Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Universidad Autónoma de Madrid (UAM) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Convex hull
Bounded set Applied Mathematics 010102 general mathematics Mathematical analysis Dimension (graph theory) Open set Mathematics::Analysis of PDEs Type (model theory) Inverse problem Mathematics::Spectral Theory 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Boundary value problem Uniqueness 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, Elsevier, 2016, 260 (3), ⟨10.1016/j.jde.2015.10.007⟩ Journal of Differential Equations, 2016, 260 (3), ⟨10.1016/j.jde.2015.10.007⟩ |
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2015.10.007⟩ |
| Popis: | International audience; This is a follow-up of a previous article where we proved local stability estimates for a potential in a Schr\"odinger equation on an open bounded set in dimension $n=3$ from the Dirichlet-to-Neumann map with partial data. The region under control was the penumbra delimited by a source of light outside of the convex hull of the open set. These local estimates provided stability of log-log type corresponding to the uniqueness results in Calder\'on's inverse problem with partial data proved by Kenig, Sj\"ostrand and Uhlmann. In this article, we prove the corresponding global estimates in all dimensions higher than three. The estimates are based on the construction of solutions of the Schr\"odinger equation by complex geometrical optics developed in the anisotropic setting by Dos Santos Ferreira, Kenig, Salo and Uhlmann to solve the Calder\'on problem in certain admissible geometries. |
| Databáze: | OpenAIRE |
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