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Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
1. | Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia |
2. | Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States |
3. | Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914 |
References:
[1] |
R. A. Adams and J. J. F. Fournier, Sobolev Spaces, $2^{nd}$ edition, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal., 27 (1988), 153-172.
doi: 10.1080/00036818808839730. |
[3] |
K. Astala, D. Faraco and K. M. Rogers, Rough potential recovery in the plane, preprint,, , ().
|
[4] |
E. Blåsten, The Inverse Problem of the Schrödinger Equation in the Plane: A Dissection of Bukhgeim's Result, Licentiate thesis, University of Helsinki, 2010. |
[5] |
E. Blåsten, On the Gel'fand-Calderón Inverse Problem in Two Dimensions, Ph.D. thesis, University of Helsinki, 2013. |
[6] |
A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl., 16 (2008), 19-33.
doi: 10.1515/jiip.2008.002. |
[7] |
L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, 1998. |
[8] |
O. Yu. Imanuvilov and M. Yamamoto, Inverse boundary value problem for linear Schrödinger equation in two dimensions, preprint,, , ().
|
[9] |
O. Yu. Imanuvilov and M. Yamamoto, Uniqueness for inverse boundary value problems, by Dirichlet-to-Neumann map on subboundaries, ().
doi: 10.1007/s00032-013-0205-3. |
[10] |
J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, New York-Heidelberg, 1972. |
[11] |
L. Liu, Stability Estimates for the Two Dimensional Inverse Conductivity Problem, Ph.D. thesis, University of Rochester, 1997. |
[12] |
N. Mandache, Exponential instability in an inverse problem for the Schrödinger equation, Inverse Problems, 17 (2001), 1435-1444.
doi: 10.1088/0266-5611/17/5/313. |
[13] |
C. Miranda, Partial Differential Equations of Elliptic Type, $2^{nd}$ revised edition, Springer-Verlag, New York-Berlin, 1970. |
[14] |
A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71-96.
doi: 10.2307/2118653. |
[15] |
R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón, inverse problem in two dimensions, ().
doi: 10.1515/JIIP.2011.003. |
[16] |
R. G. Novikov and M. Santacesaria, Global uniqueness and reconstruction for the, multi-channel Gel'fand-Calderón inverse problem in two dimensions., ().
doi: 10.1016/j.bulsci.2011.04.007. |
[17] |
M. Santacesaria, New global stability estimates for the Calderón problem in two dimensions, J. Inst. Math. Jussieu, 12 (2013), 553-569.
doi: 10.1017/S147474801200076X. |
[18] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value, problem., ().
doi: 10.2307/1971291. |
[19] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011, 39 pp.
doi: 10.1088/0266-5611/25/12/123011. |
[20] |
I. N. Vekua, Generalized Analytic Functions, Pergamon Press, London-Paris-Frankfurt, 1962. |
show all references
References:
[1] |
R. A. Adams and J. J. F. Fournier, Sobolev Spaces, $2^{nd}$ edition, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal., 27 (1988), 153-172.
doi: 10.1080/00036818808839730. |
[3] |
K. Astala, D. Faraco and K. M. Rogers, Rough potential recovery in the plane, preprint,, , ().
|
[4] |
E. Blåsten, The Inverse Problem of the Schrödinger Equation in the Plane: A Dissection of Bukhgeim's Result, Licentiate thesis, University of Helsinki, 2010. |
[5] |
E. Blåsten, On the Gel'fand-Calderón Inverse Problem in Two Dimensions, Ph.D. thesis, University of Helsinki, 2013. |
[6] |
A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl., 16 (2008), 19-33.
doi: 10.1515/jiip.2008.002. |
[7] |
L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, 1998. |
[8] |
O. Yu. Imanuvilov and M. Yamamoto, Inverse boundary value problem for linear Schrödinger equation in two dimensions, preprint,, , ().
|
[9] |
O. Yu. Imanuvilov and M. Yamamoto, Uniqueness for inverse boundary value problems, by Dirichlet-to-Neumann map on subboundaries, ().
doi: 10.1007/s00032-013-0205-3. |
[10] |
J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, New York-Heidelberg, 1972. |
[11] |
L. Liu, Stability Estimates for the Two Dimensional Inverse Conductivity Problem, Ph.D. thesis, University of Rochester, 1997. |
[12] |
N. Mandache, Exponential instability in an inverse problem for the Schrödinger equation, Inverse Problems, 17 (2001), 1435-1444.
doi: 10.1088/0266-5611/17/5/313. |
[13] |
C. Miranda, Partial Differential Equations of Elliptic Type, $2^{nd}$ revised edition, Springer-Verlag, New York-Berlin, 1970. |
[14] |
A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71-96.
doi: 10.2307/2118653. |
[15] |
R. G. Novikov and M. Santacesaria, A global stability estimate for the Gel'fand-Calderón, inverse problem in two dimensions, ().
doi: 10.1515/JIIP.2011.003. |
[16] |
R. G. Novikov and M. Santacesaria, Global uniqueness and reconstruction for the, multi-channel Gel'fand-Calderón inverse problem in two dimensions., ().
doi: 10.1016/j.bulsci.2011.04.007. |
[17] |
M. Santacesaria, New global stability estimates for the Calderón problem in two dimensions, J. Inst. Math. Jussieu, 12 (2013), 553-569.
doi: 10.1017/S147474801200076X. |
[18] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value, problem., ().
doi: 10.2307/1971291. |
[19] |
G. Uhlmann, Electrical impedance tomography and Calderón's problem, Inverse Problems, 25 (2009), 123011, 39 pp.
doi: 10.1088/0266-5611/25/12/123011. |
[20] |
I. N. Vekua, Generalized Analytic Functions, Pergamon Press, London-Paris-Frankfurt, 1962. |
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