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Stability of the Calderón problem in admissible geometries
Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem
1. | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States |
References:
[1] |
A. L. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, Comm. PDE, 27 (2002), 653-668.
doi: 10.1081/PDE-120002868. |
[2] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasileira de Matemática, Río de Janeiro, 1980, 65-73. |
[3] |
F. J. Chung, A partial data result for the magnetic Schrödinger inverse problem, Anal. and PDE, 7 (2014), 117-157.
doi: 10.2140/apde.2014.7.117. |
[4] |
F. J. Chung, Partial data for the Neumann-to-Dirichlet map, preprint, arXiv:1211.0211, (2012). |
[5] |
F. J. Chung, M. Salo and L. Tzou, Partial data inverse problems for the Hodge Laplacian, preprint, arXiv:1310.4616, (2013). |
[6] |
D. Dos Santos Ferreira, C. E. Kenig, M. Salo and G. Uhlmann, Limiting Carleman weights and anisotropic inverse problems, Invent. Math., 178 (2009), 119-171.
doi: 10.1007/s00222-009-0196-4. |
[7] |
D. Dos Santos Ferreira, C. E. Kenig, J. Sjöstrand and G. Uhlmann, Determining a magnetic Schrödinger operator from partial Cauchy data, Comm. Math. Phys., 271 (2007), 467-488.
doi: 10.1007/s00220-006-0151-9. |
[8] |
N. Hyvönen, P. Piiroinen and O. Seiskari, Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane, SIAM J. Math. Anal., 44 (2012), 3526-3536. arXiv:1204.0346.
doi: 10.1137/120872164. |
[9] |
O. Imanuvilov, G. Uhlmann and M. Yamamoto, The Calderón problem with partial data in two dimensions, J. Amer. Math. Soc., 23 (2010), 655-691.
doi: 10.1090/S0894-0347-10-00656-9. |
[10] |
O. Imanuvilov, G. Uhlmann and M. Yamamoto, Inverse boundary value problem by partial data for Neumann-to-Dirichlet-map in two dimensions, preprint, arXiv:1210.1255. |
[11] |
V. Isakov, On uniqueness in the inverse conductivity problem with local data, Inverse Probl. Imaging, 1 (2007), 95-105.
doi: 10.3934/ipi.2007.1.95. |
[12] |
C. E. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Anal. and PDE, 6 (2013), 2003-2048.
doi: 10.2140/apde.2013.6.2003. |
[13] |
C. E. Kenig and M. Salo, Recent progress in the Calderón problem with partial data, Contemp. Math., 615 (2014), 193-222.
doi: 10.1090/conm/615/12245. |
[14] |
C. E. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data, Ann. of Math., 165 (2007), 567-591.
doi: 10.4007/annals.2007.165.567. |
[15] |
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, Comm. Math. Phys., 312 (2012), 87-126.
doi: 10.1007/s00220-012-1431-1. |
[16] |
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. |
[17] |
G. Nakamura, Z. Sun and G. Uhlmann, Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field, Math. Ann., 303 (1995), 377-388.
doi: 10.1007/BF01460996. |
[18] |
V. Pohjola, An inverse problem for the magnetic Schrödinger operator on a half space with partial data, preprint, arXiv:1302.7265, (2013). |
[19] |
M. Salo, Inverse problems for nonsmooth first order perturbations of the Laplacian, Ann. Acad. Sci. Fenn. Math. Diss., 139 (2004), 67 pp. |
[20] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153-169.
doi: 10.2307/1971291. |
[21] |
M. E. Taylor, Partial Differential Equations I: Basic Theory, Applied Mathematical Sciences, 115, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4684-9320-7. |
[22] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inv. Prob., 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
[23] |
M. Zworski, Semiclassical Analysis, Graduate Studies in Mathematics, 138, American Mathematical Society, Providence, RI, 2012. |
show all references
References:
[1] |
A. L. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, Comm. PDE, 27 (2002), 653-668.
doi: 10.1081/PDE-120002868. |
[2] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasileira de Matemática, Río de Janeiro, 1980, 65-73. |
[3] |
F. J. Chung, A partial data result for the magnetic Schrödinger inverse problem, Anal. and PDE, 7 (2014), 117-157.
doi: 10.2140/apde.2014.7.117. |
[4] |
F. J. Chung, Partial data for the Neumann-to-Dirichlet map, preprint, arXiv:1211.0211, (2012). |
[5] |
F. J. Chung, M. Salo and L. Tzou, Partial data inverse problems for the Hodge Laplacian, preprint, arXiv:1310.4616, (2013). |
[6] |
D. Dos Santos Ferreira, C. E. Kenig, M. Salo and G. Uhlmann, Limiting Carleman weights and anisotropic inverse problems, Invent. Math., 178 (2009), 119-171.
doi: 10.1007/s00222-009-0196-4. |
[7] |
D. Dos Santos Ferreira, C. E. Kenig, J. Sjöstrand and G. Uhlmann, Determining a magnetic Schrödinger operator from partial Cauchy data, Comm. Math. Phys., 271 (2007), 467-488.
doi: 10.1007/s00220-006-0151-9. |
[8] |
N. Hyvönen, P. Piiroinen and O. Seiskari, Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane, SIAM J. Math. Anal., 44 (2012), 3526-3536. arXiv:1204.0346.
doi: 10.1137/120872164. |
[9] |
O. Imanuvilov, G. Uhlmann and M. Yamamoto, The Calderón problem with partial data in two dimensions, J. Amer. Math. Soc., 23 (2010), 655-691.
doi: 10.1090/S0894-0347-10-00656-9. |
[10] |
O. Imanuvilov, G. Uhlmann and M. Yamamoto, Inverse boundary value problem by partial data for Neumann-to-Dirichlet-map in two dimensions, preprint, arXiv:1210.1255. |
[11] |
V. Isakov, On uniqueness in the inverse conductivity problem with local data, Inverse Probl. Imaging, 1 (2007), 95-105.
doi: 10.3934/ipi.2007.1.95. |
[12] |
C. E. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Anal. and PDE, 6 (2013), 2003-2048.
doi: 10.2140/apde.2013.6.2003. |
[13] |
C. E. Kenig and M. Salo, Recent progress in the Calderón problem with partial data, Contemp. Math., 615 (2014), 193-222.
doi: 10.1090/conm/615/12245. |
[14] |
C. E. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data, Ann. of Math., 165 (2007), 567-591.
doi: 10.4007/annals.2007.165.567. |
[15] |
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, Comm. Math. Phys., 312 (2012), 87-126.
doi: 10.1007/s00220-012-1431-1. |
[16] |
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. |
[17] |
G. Nakamura, Z. Sun and G. Uhlmann, Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field, Math. Ann., 303 (1995), 377-388.
doi: 10.1007/BF01460996. |
[18] |
V. Pohjola, An inverse problem for the magnetic Schrödinger operator on a half space with partial data, preprint, arXiv:1302.7265, (2013). |
[19] |
M. Salo, Inverse problems for nonsmooth first order perturbations of the Laplacian, Ann. Acad. Sci. Fenn. Math. Diss., 139 (2004), 67 pp. |
[20] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153-169.
doi: 10.2307/1971291. |
[21] |
M. E. Taylor, Partial Differential Equations I: Basic Theory, Applied Mathematical Sciences, 115, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4684-9320-7. |
[22] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inv. Prob., 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
[23] |
M. Zworski, Semiclassical Analysis, Graduate Studies in Mathematics, 138, American Mathematical Society, Providence, RI, 2012. |
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