- Previous Article
- IPI Home
- This Issue
-
Next Article
The nonlinear Fourier transform for two-dimensional subcritical potentials
An inverse problem for the magnetic Schrödinger operator on a half space with partial data
1. | Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hallstromin katu 2b) FI-00014, Finland |
References:
[1] |
S. Arridge, Optical tomography in medical imaging, Inverse Problems, 15 (1999), R41-R93.
doi: 10.1088/0266-5611/15/2/022. |
[2] |
M. Cheney and D. Isaacson, Inverse problems for a perturbed dissipative half-space, Inverse Problems, 11 (1995), 865-888.
doi: 10.1088/0266-5611/11/4/015. |
[3] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques, Springer-Verlag, Berlin, 2009.
doi: 10.1007/978-3-642-02460-3. |
[4] |
F. J. Chung, A partial data result for the magnetic Schrödinger inverse problem, Anal. PDE, 7 (2014), 117-157. arXiv:1111.6658.
doi: 10.2140/apde.2014.7.117. |
[5] |
D. Dos Santos Ferreira, C. E. Kenig, J. Sjöstrand and G. Uhlmann, Determining a magnetic Schrödinger operator from partial Cauchy data, Communications in Mathematical Physics, 271 (2007), 467-488.
doi: 10.1007/s00220-006-0151-9. |
[6] |
G. Eskin and J. Ralston, Inverse scattering problem for the Schrödinger equation with magentic potential at a fixed energy, Communications in Mathematicala Physics, 173 (1995), 199-224.
doi: 10.1007/BF02100187. |
[7] |
L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1990. |
[8] |
V. Isakov, On uniqueness in the inverse conductivity problem with local data, Inverse Problems and Imaging, 1 (2007), 95-105.
doi: 10.3934/ipi.2007.1.95. |
[9] |
K. Knudsen and M. Salo, Determining nonsmooth first order terms from partial boundary measurements, Inverse Problems and Imaging, 1 (2007), 349-369.
doi: 10.3934/ipi.2007.1.349. |
[10] |
R. Kress, Linear Integral Equations, Springer, Berlin, 1989.
doi: 10.1007/978-3-642-97146-4. |
[11] |
K. Krupchyk, M. Lassas and G. Uhlmann, Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain, Communications in Mathematical Physics, 312 (2012), 87-126.
doi: 10.1007/s00220-012-1431-1. |
[12] |
K. Krupchyk and G. Uhlmann, Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential, Comm. Math. Phys., 327 (2014), 993-1009.
doi: 10.1007/s00220-014-1942-z. |
[13] |
M. Lassas, M. Cheney and G. Uhlmann, Uniqueness for a wave propagation inverse problem in a half-space, Inverse Problems, 14 (1998), 679-684.
doi: 10.1088/0266-5611/14/3/017. |
[14] |
R. Leis, Initial Boundary Values Problems in Mathematical Physics, John Wiley and Sons Ltd., Stuttgart, 1986.
doi: 10.1007/978-3-663-10649-4. |
[15] |
X. Li, Inverse boundary value problems with partial data in unbounded domains, Inverse Problems, 28 (2012), 1-23.
doi: 10.1088/0266-5611/28/8/085003. |
[16] |
X. Li and G. Uhlmann, Inverse problems with partial data in a slab, Inverse Problems and Imaging, 4 (2010), 449-462.
doi: 10.3934/ipi.2010.4.449. |
[17] |
G. Nakamura, Z. Sun and G. Uhlmann, Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field, Mathematische Annalen, 303 (1995), 377-388.
doi: 10.1007/BF01460996. |
[18] |
A. Panchenko, An inverse problem for the magnetic schrödinger equation and quasi-exponential solutions of nonsmooth partial differential equations, Inverse Problems, 18 (2002), 1421-1434.
doi: 10.1088/0266-5611/18/5/314. |
[19] |
V. Pohjola, An Inverse Boundary Value Problem for the Magnetic Schrödinger Operator on a Half Space, preprint, 2012, arXiv:1209.0982. |
[20] |
M. Salo, Inverse problems for nonsmooth first order perturbations of the Laplacian, Ann. Acad. Sci. Fenn. Math. Diss., 139, 2004, 67 pp. |
[21] |
M. Salo, Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field, Communications in Partial Differential Equations, 31 (2006), 1639-1666.
doi: 10.1080/03605300500530420. |
[22] |
Z. Sun, An inverse boundary problem for Schrödinger operators with vector potentials, Trans. Amer. Math.Soc., 338 (1993), 953-969.
doi: 10.2307/2154438. |
[23] |
C. Tolmasky, Exponentially growing solutions for nonsmooth first-order perturbations of the laplacian, SIAM J. Math. Anal., 29 (1998), 116-133.
doi: 10.1137/S0036141096301038. |
[24] |
G. Uhlmann, electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
show all references
References:
[1] |
S. Arridge, Optical tomography in medical imaging, Inverse Problems, 15 (1999), R41-R93.
doi: 10.1088/0266-5611/15/2/022. |
[2] |
M. Cheney and D. Isaacson, Inverse problems for a perturbed dissipative half-space, Inverse Problems, 11 (1995), 865-888.
doi: 10.1088/0266-5611/11/4/015. |
[3] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques, Springer-Verlag, Berlin, 2009.
doi: 10.1007/978-3-642-02460-3. |
[4] |
F. J. Chung, A partial data result for the magnetic Schrödinger inverse problem, Anal. PDE, 7 (2014), 117-157. arXiv:1111.6658.
doi: 10.2140/apde.2014.7.117. |
[5] |
D. Dos Santos Ferreira, C. E. Kenig, J. Sjöstrand and G. Uhlmann, Determining a magnetic Schrödinger operator from partial Cauchy data, Communications in Mathematical Physics, 271 (2007), 467-488.
doi: 10.1007/s00220-006-0151-9. |
[6] |
G. Eskin and J. Ralston, Inverse scattering problem for the Schrödinger equation with magentic potential at a fixed energy, Communications in Mathematicala Physics, 173 (1995), 199-224.
doi: 10.1007/BF02100187. |
[7] |
L. Hörmander, An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1990. |
[8] |
V. Isakov, On uniqueness in the inverse conductivity problem with local data, Inverse Problems and Imaging, 1 (2007), 95-105.
doi: 10.3934/ipi.2007.1.95. |
[9] |
K. Knudsen and M. Salo, Determining nonsmooth first order terms from partial boundary measurements, Inverse Problems and Imaging, 1 (2007), 349-369.
doi: 10.3934/ipi.2007.1.349. |
[10] |
R. Kress, Linear Integral Equations, Springer, Berlin, 1989.
doi: 10.1007/978-3-642-97146-4. |
[11] |
K. Krupchyk, M. Lassas and G. Uhlmann, Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain, Communications in Mathematical Physics, 312 (2012), 87-126.
doi: 10.1007/s00220-012-1431-1. |
[12] |
K. Krupchyk and G. Uhlmann, Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential, Comm. Math. Phys., 327 (2014), 993-1009.
doi: 10.1007/s00220-014-1942-z. |
[13] |
M. Lassas, M. Cheney and G. Uhlmann, Uniqueness for a wave propagation inverse problem in a half-space, Inverse Problems, 14 (1998), 679-684.
doi: 10.1088/0266-5611/14/3/017. |
[14] |
R. Leis, Initial Boundary Values Problems in Mathematical Physics, John Wiley and Sons Ltd., Stuttgart, 1986.
doi: 10.1007/978-3-663-10649-4. |
[15] |
X. Li, Inverse boundary value problems with partial data in unbounded domains, Inverse Problems, 28 (2012), 1-23.
doi: 10.1088/0266-5611/28/8/085003. |
[16] |
X. Li and G. Uhlmann, Inverse problems with partial data in a slab, Inverse Problems and Imaging, 4 (2010), 449-462.
doi: 10.3934/ipi.2010.4.449. |
[17] |
G. Nakamura, Z. Sun and G. Uhlmann, Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field, Mathematische Annalen, 303 (1995), 377-388.
doi: 10.1007/BF01460996. |
[18] |
A. Panchenko, An inverse problem for the magnetic schrödinger equation and quasi-exponential solutions of nonsmooth partial differential equations, Inverse Problems, 18 (2002), 1421-1434.
doi: 10.1088/0266-5611/18/5/314. |
[19] |
V. Pohjola, An Inverse Boundary Value Problem for the Magnetic Schrödinger Operator on a Half Space, preprint, 2012, arXiv:1209.0982. |
[20] |
M. Salo, Inverse problems for nonsmooth first order perturbations of the Laplacian, Ann. Acad. Sci. Fenn. Math. Diss., 139, 2004, 67 pp. |
[21] |
M. Salo, Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field, Communications in Partial Differential Equations, 31 (2006), 1639-1666.
doi: 10.1080/03605300500530420. |
[22] |
Z. Sun, An inverse boundary problem for Schrödinger operators with vector potentials, Trans. Amer. Math.Soc., 338 (1993), 953-969.
doi: 10.2307/2154438. |
[23] |
C. Tolmasky, Exponentially growing solutions for nonsmooth first-order perturbations of the laplacian, SIAM J. Math. Anal., 29 (1998), 116-133.
doi: 10.1137/S0036141096301038. |
[24] |
G. Uhlmann, electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
[1] |
Sombuddha Bhattacharyya. An inverse problem for the magnetic Schrödinger operator on Riemannian manifolds from partial boundary data. Inverse Problems and Imaging, 2018, 12 (3) : 801-830. doi: 10.3934/ipi.2018034 |
[2] |
Ru-Yu Lai. Global uniqueness for an inverse problem for the magnetic Schrödinger operator. Inverse Problems and Imaging, 2011, 5 (1) : 59-73. doi: 10.3934/ipi.2011.5.59 |
[3] |
Francis J. Chung. Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem. Inverse Problems and Imaging, 2014, 8 (4) : 959-989. doi: 10.3934/ipi.2014.8.959 |
[4] |
Leyter Potenciano-Machado, Alberto Ruiz. Stability estimates for a magnetic Schrödinger operator with partial data. Inverse Problems and Imaging, 2018, 12 (6) : 1309-1342. doi: 10.3934/ipi.2018055 |
[5] |
Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems and Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469 |
[6] |
Boya Liu. Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies. Inverse Problems and Imaging, 2020, 14 (5) : 783-796. doi: 10.3934/ipi.2020036 |
[7] |
Türker Özsarı, Nermin Yolcu. The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3285-3316. doi: 10.3934/cpaa.2019148 |
[8] |
Joel Andersson, Leo Tzou. Stability for a magnetic Schrödinger operator on a Riemann surface with boundary. Inverse Problems and Imaging, 2018, 12 (1) : 1-28. doi: 10.3934/ipi.2018001 |
[9] |
Xing-Bin Pan. An eigenvalue variation problem of magnetic Schrödinger operator in three dimensions. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 933-978. doi: 10.3934/dcds.2009.24.933 |
[10] |
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042 |
[11] |
Corentin Audiard. On the non-homogeneous boundary value problem for Schrödinger equations. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 3861-3884. doi: 10.3934/dcds.2013.33.3861 |
[12] |
Ran Zhuo, Fengquan Li, Boqiang Lv. Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space. Communications on Pure and Applied Analysis, 2014, 13 (3) : 977-990. doi: 10.3934/cpaa.2014.13.977 |
[13] |
Eemeli Blåsten, Oleg Yu. Imanuvilov, Masahiro Yamamoto. Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials. Inverse Problems and Imaging, 2015, 9 (3) : 709-723. doi: 10.3934/ipi.2015.9.709 |
[14] |
Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems and Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297 |
[15] |
Victor Isakov. On uniqueness in the inverse conductivity problem with local data. Inverse Problems and Imaging, 2007, 1 (1) : 95-105. doi: 10.3934/ipi.2007.1.95 |
[16] |
Hisashi Morioka. Inverse boundary value problems for discrete Schrödinger operators on the multi-dimensional square lattice. Inverse Problems and Imaging, 2011, 5 (3) : 715-730. doi: 10.3934/ipi.2011.5.715 |
[17] |
Yavar Kian, Morgan Morancey, Lauri Oksanen. Application of the boundary control method to partial data Borg-Levinson inverse spectral problem. Mathematical Control and Related Fields, 2019, 9 (2) : 289-312. doi: 10.3934/mcrf.2019015 |
[18] |
Marta García-Huidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313-319. doi: 10.3934/proc.2003.2003.313 |
[19] |
Chuan-Fu Yang, Natalia Pavlovna Bondarenko. A partial inverse problem for the Sturm-Liouville operator on the lasso-graph. Inverse Problems and Imaging, 2019, 13 (1) : 69-79. doi: 10.3934/ipi.2019004 |
[20] |
Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems and Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]