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A partial data result for less regular conductivities in admissible geometries
1. | University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, United States |
References:
[1] |
K. Astala and L. Päivärinta, Calderón's inverse conductivity problem in the plane, Ann. of Math., 163 (2006), 265-299.
doi: 10.4007/annals.2006.163.265. |
[2] |
A. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, in Comm. Partial Differential Equations, 27 (2002), 653-668.
doi: 10.1081/PDE-120002868. |
[3] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), Soc. Brasil. Mat., Rio de Janeiro, 1980, 65-73. |
[4] |
P. Caro and K. M. Rogers, Global uniqueness for the Calderón problem with Lipschitz conductivities, preprint, arXiv:1411.8001. |
[5] |
D. Dos Santos Ferreira, C. E. Kenig and M. Salo, Determining an unbounded potential from Cauchy data in admissible geometries, Comm. Partial Differential Equations, 38 (2013), 50-68.
doi: 10.1080/03605302.2012.736911. |
[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] |
B. Haberman and D. Tataru, Uniqueness in Calderón's problem with Lipschitz conductivities, Duke Math. J., 162 (2013), 496-516.
doi: 10.1215/00127094-2019591. |
[8] |
B. Haberman, Uniqueness in Calderón's problems for conductivities with unbounded gradient, Comm. Math. Phys., 340 (2015), 639-659.
doi: 10.1007/s00220-015-2460-3. |
[9] |
C. E. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Anal. PDE, 6 (2013), 2003-2048.
doi: 10.2140/apde.2013.6.2003. |
[10] |
C. E. Kenig, M. Salo and G. Uhlmann, Inverse problems for the anisotropic Maxwell equations, Duke Math. J., 157 (2011), 369-419.
doi: 10.1215/00127094-1272903. |
[11] |
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. |
[12] |
K. Knudsen, The Calderón problem with partial data for less smooth conductivities, Comm. Partial Differential Equations, 31 (2006), 57-71.
doi: 10.1080/03605300500361610. |
[13] |
K. Knudsen and M. Salo, Determining nonsmooth first order terms from partial boundary measurements, Inverse Probl. Imaging, 1 (2007), 349-369.
doi: 10.3934/ipi.2007.1.349. |
[14] |
M. Salo, Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field, Comm. Partial Differential Equations, 31 (2006), 1639-1666.
doi: 10.1080/03605300500530420. |
[15] |
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. |
[16] |
C. F. Tomalsky, Exponentially growing solutions for nonsmooth first-order perturbations of the Laplacian, SIAM J. Math. Anal., 29 (1998), 116-133.
doi: 10.1137/S0036141096301038. |
[17] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
[18] |
G. Zhang, Uniqueness in the Calderón problem with partial data for less smooth conductivities, Inverse Problems, 28 (2012), 105008, 18pp.
doi: 10.1088/0266-5611/28/10/105008. |
show all references
References:
[1] |
K. Astala and L. Päivärinta, Calderón's inverse conductivity problem in the plane, Ann. of Math., 163 (2006), 265-299.
doi: 10.4007/annals.2006.163.265. |
[2] |
A. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, in Comm. Partial Differential Equations, 27 (2002), 653-668.
doi: 10.1081/PDE-120002868. |
[3] |
A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), Soc. Brasil. Mat., Rio de Janeiro, 1980, 65-73. |
[4] |
P. Caro and K. M. Rogers, Global uniqueness for the Calderón problem with Lipschitz conductivities, preprint, arXiv:1411.8001. |
[5] |
D. Dos Santos Ferreira, C. E. Kenig and M. Salo, Determining an unbounded potential from Cauchy data in admissible geometries, Comm. Partial Differential Equations, 38 (2013), 50-68.
doi: 10.1080/03605302.2012.736911. |
[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] |
B. Haberman and D. Tataru, Uniqueness in Calderón's problem with Lipschitz conductivities, Duke Math. J., 162 (2013), 496-516.
doi: 10.1215/00127094-2019591. |
[8] |
B. Haberman, Uniqueness in Calderón's problems for conductivities with unbounded gradient, Comm. Math. Phys., 340 (2015), 639-659.
doi: 10.1007/s00220-015-2460-3. |
[9] |
C. E. Kenig and M. Salo, The Calderón problem with partial data on manifolds and applications, Anal. PDE, 6 (2013), 2003-2048.
doi: 10.2140/apde.2013.6.2003. |
[10] |
C. E. Kenig, M. Salo and G. Uhlmann, Inverse problems for the anisotropic Maxwell equations, Duke Math. J., 157 (2011), 369-419.
doi: 10.1215/00127094-1272903. |
[11] |
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. |
[12] |
K. Knudsen, The Calderón problem with partial data for less smooth conductivities, Comm. Partial Differential Equations, 31 (2006), 57-71.
doi: 10.1080/03605300500361610. |
[13] |
K. Knudsen and M. Salo, Determining nonsmooth first order terms from partial boundary measurements, Inverse Probl. Imaging, 1 (2007), 349-369.
doi: 10.3934/ipi.2007.1.349. |
[14] |
M. Salo, Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field, Comm. Partial Differential Equations, 31 (2006), 1639-1666.
doi: 10.1080/03605300500530420. |
[15] |
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. |
[16] |
C. F. Tomalsky, Exponentially growing solutions for nonsmooth first-order perturbations of the Laplacian, SIAM J. Math. Anal., 29 (1998), 116-133.
doi: 10.1137/S0036141096301038. |
[17] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011.
doi: 10.1088/0266-5611/25/12/123011. |
[18] |
G. Zhang, Uniqueness in the Calderón problem with partial data for less smooth conductivities, Inverse Problems, 28 (2012), 105008, 18pp.
doi: 10.1088/0266-5611/28/10/105008. |
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