Monotonicity-based inversion of the fractional Schr\"odinger equation
By Bastian von Harrach, Yi-Hsuan Lin. 2017
55 citations recorded by the source corpus.
We consider the inverse problems of for the fractional Schr\"{o}dinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calder\'{o}n problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension $n\geq 2$ and only requires the background solution of the fractional Schr\"{o}dinger equation.
Subfields: Biomedical Engineering, Mathematical Physics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/d3ac90deb1f640e4c5686e8de6aca48e626721d1
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In Biomedical Engineering
- Mikko Salo
- Tuhin Ghosh
- Gunther Uhlmann
- Yi-Hsuan Lin
- Jesse Railo
- Keijo Monkkonen
- Giovanni Covi
- Ru-Yu Lai
In Mathematical Physics
- Mikko Salo
- Gunther Uhlmann
- Tuhin Ghosh
- Yi-Hsuan Lin
- Katya Krupchyk
- Jesse Railo
- Keijo Monkkonen
- Giovanni Covi
In Modeling and Simulation
Citations in the corpus
- The Calderón problem for the fractional Schrödinger equation (2016, background): “2017], semilinear equations [Lai and Lin 2019], reconstruction and shape detection [Harrach and Lin 2017; Cao et al. 2019; Ghosh et al. 2018], and quantitative Runge approximation [Rüland and Salo 2019b; 2020].”