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Calderón problem for Maxwell's equations in cylindrical domain
1. | Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States |
2. | Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914 |
References:
[1] |
J. Boman and E. T. Quinto, Support theorems for real-analytic Radon transforms, Duke Math. J., 55 (1987), 943-948.
doi: 10.1215/S0012-7094-87-05547-5. |
[2] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73, Soc. Brasil. Mat., Río de Janeiro, 1980. |
[3] |
P. Caro, P. Ola and M. Salo, Inverse boundary value problem for Maxwell equations with local data, Comm. P.D.E., 34 (2009), 1425-1464.
doi: 10.1080/03605300903296272. |
[4] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1990. |
[5] |
S. Helgason, Integral Geometry and Radon Transforms, Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-1-4419-6055-9. |
[6] |
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. |
[7] |
O. Imanuvilov and M. Yamamoto, Inverse boundary value problem for the Schrödinger equation in cylindrical domain by partial boundary data, Inverse Problems , 29 (2013), 045002, 8pp.
doi: 10.1088/0266-5611/29/4/045002. |
[8] |
O. Imanuvilov and M. Yamamoto, Uniqueness for inverse boundary value problems by Dirichlet-to-Neumann map on subboundaries, Milan J. Math., 81 (2013), 187-258.
doi: 10.1007/s00032-013-0205-3. |
[9] |
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. |
[10] |
C. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Mathematical Subject Classification, 6 (2013), 2003-2048. arXiv:1211.1054.
doi: 10.2140/apde.2013.6.2003. |
[11] |
A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71-96.
doi: 10.2307/2118653. |
[12] |
P. Ola, L. Päivärinta and E. Somersalo, An inverse boundary value problem in electrodynamics, Duke . Math. J., 70 (1993), 617-653.
doi: 10.1215/S0012-7094-93-07014-7. |
[13] |
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. |
show all references
References:
[1] |
J. Boman and E. T. Quinto, Support theorems for real-analytic Radon transforms, Duke Math. J., 55 (1987), 943-948.
doi: 10.1215/S0012-7094-87-05547-5. |
[2] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73, Soc. Brasil. Mat., Río de Janeiro, 1980. |
[3] |
P. Caro, P. Ola and M. Salo, Inverse boundary value problem for Maxwell equations with local data, Comm. P.D.E., 34 (2009), 1425-1464.
doi: 10.1080/03605300903296272. |
[4] |
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1990. |
[5] |
S. Helgason, Integral Geometry and Radon Transforms, Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-1-4419-6055-9. |
[6] |
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. |
[7] |
O. Imanuvilov and M. Yamamoto, Inverse boundary value problem for the Schrödinger equation in cylindrical domain by partial boundary data, Inverse Problems , 29 (2013), 045002, 8pp.
doi: 10.1088/0266-5611/29/4/045002. |
[8] |
O. Imanuvilov and M. Yamamoto, Uniqueness for inverse boundary value problems by Dirichlet-to-Neumann map on subboundaries, Milan J. Math., 81 (2013), 187-258.
doi: 10.1007/s00032-013-0205-3. |
[9] |
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. |
[10] |
C. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Mathematical Subject Classification, 6 (2013), 2003-2048. arXiv:1211.1054.
doi: 10.2140/apde.2013.6.2003. |
[11] |
A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71-96.
doi: 10.2307/2118653. |
[12] |
P. Ola, L. Päivärinta and E. Somersalo, An inverse boundary value problem in electrodynamics, Duke . Math. J., 70 (1993), 617-653.
doi: 10.1215/S0012-7094-93-07014-7. |
[13] |
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. |
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