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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.
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.
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), 65.
|
[4] |
P. Caro and K. M. Rogers, Global uniqueness for the Calderón problem with Lipschitz conductivities, preprint,, , (). Google Scholar |
[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.
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.
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.
doi: 10.1215/00127094-2019591. |
[8] |
B. Haberman, Uniqueness in Calderón's problems for conductivities with unbounded gradient,, Comm. Math. Phys., 340 (2015), 639.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1137/S0036141096301038. |
[17] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem,, Inverse Problems, 25 (2009).
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).
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.
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.
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), 65.
|
[4] |
P. Caro and K. M. Rogers, Global uniqueness for the Calderón problem with Lipschitz conductivities, preprint,, , (). Google Scholar |
[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.
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.
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.
doi: 10.1215/00127094-2019591. |
[8] |
B. Haberman, Uniqueness in Calderón's problems for conductivities with unbounded gradient,, Comm. Math. Phys., 340 (2015), 639.
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.
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.
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.
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.
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.
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.
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.
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.
doi: 10.1137/S0036141096301038. |
[17] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem,, Inverse Problems, 25 (2009).
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).
doi: 10.1088/0266-5611/28/10/105008. |
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