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Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

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  • We consider inverse boundary value problems for the Schrödinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within $L^p$-class of potentials with $p>2$.
    Mathematics Subject Classification: Primary: 35R30, 30G20; Secondary: 35J10.

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  • [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, arXiv:1304.1317.

    [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, arXiv:1208.3775.

    [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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