Determination of lower order perturbations of a polyharmonic operator in two dimensions

References

[1] K. Astala and L. Päivärinta, Calderón’s inverse conductivity problem in the plane, Ann. of Math. (2) 163 (2006), no. 1, 265–299. 10.4007/annals.2006.163.265Search in Google Scholar

[2] S. Bhattacharyya and T. Ghosh, Inverse boundary value problem of determining up to a second order tensor appear in the lower order perturbation of a polyharmonic operator, J. Fourier Anal. Appl. 25 (2019), no. 3, 661–683. 10.1007/s00041-018-9625-3Search in Google Scholar

[3] S. Bhattacharyya and T. Ghosh, An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator, Math. Ann. 384 (2022), no. 1–2, 457–489. 10.1007/s00208-021-02276-6Search in Google Scholar

[4] S. Bhattacharyya, V. P. Krishnan and S. K. Sahoo, Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data, preprint (2021), https://arxiv.org/abs/2111.07610. Search in Google Scholar

[5] E. Blåsten, The inverse problem of the Schrödinger equation in the plane; a dissection of Bukhgeim’s result, preprint (2011), https://arxiv.org/abs/1103.6200. Search in Google Scholar

[6] R. M. Brown and G. A. Uhlmann, Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions, Comm. Partial Differential Equations 22 (1997), no. 5–6, 1009–1027. 10.1080/03605309708821292Search in Google Scholar

[7] A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inverse Ill-Posed Probl. 16 (2008), no. 1, 19–33. 10.1515/jiip.2008.002Search in Google Scholar

[8] A.-P. Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro 1980), Brazilian Mathematical Society, Rio de Janeiro (1980), 65–73. Search in Google Scholar

[9] F. Gazzola, H.-C. Grunau and G. Sweers, Polyharmonic Boundary Value Problems, Lecture Notes in Math. 1991, Springer, Berlin, 2010. 10.1007/978-3-642-12245-3Search in Google Scholar

[10] T. Ghosh and V. P. Krishnan, Determination of lower order perturbations of the polyharmonic operator from partial boundary data, Appl. Anal. 95 (2016), no. 11, 2444–2463. 10.1080/00036811.2015.1092522Search in Google Scholar

[11] C. Guillarmou and L. Tzou, Calderón inverse problem with partial data on Riemann surfaces, Duke Math. J. 158 (2011), no. 1, 83–120. 10.1215/00127094-1276310Search in Google Scholar

[12] C. Guillarmou and L. Tzou, Identification of a connection from Cauchy data on a Riemann surface with boundary, Geom. Funct. Anal. 21 (2011), no. 2, 393–418. 10.1007/s00039-011-0110-2Search in Google Scholar

[13] C. Guillarmou and L. Tzou, The Calderón inverse problem in two dimensions, Inverse Problems and Applications: Inside Out. II, Math. Sci. Res. Inst. Publ. 60, Cambridge University, Cambridge (2013), 119–166. Search in Google Scholar

[14] M. Ikehata, A special Green’s function for the biharmonic operator and its application to an inverse boundary value problem, Comput. Math. Appl. 22 (1991), no. 4–5, 53–66. 10.1016/0898-1221(91)90131-MSearch in Google Scholar

[15] M. Ikehata, An inverse problem for the plate in the Love–Kirchhoff theory, SIAM J. Appl. Math. 53 (1993), no. 4, 942–970. 10.1137/0153047Search in Google Scholar

[16] M. Ikehata, A relationship between two Dirichlet to Neumann maps in anisotropic elastic plate theory, J. Inverse Ill-Posed Probl. 4 (1996), no. 3, 233–243. 10.1515/jiip.1996.4.3.233Search in Google Scholar

[17] O. Y. Imanuvilov, G. Uhlmann and M. Yamamoto, The Calderón problem with partial data in two dimensions, J. Amer. Math. Soc. 23 (2010), no. 3, 655–691. 10.1090/S0894-0347-10-00656-9Search in Google Scholar

[18] O. Y. Imanuvilov, G. Uhlmann and M. Yamamoto, Partial Cauchy data for general second order elliptic operators in two dimensions, Publ. Res. Inst. Math. Sci. 48 (2012), no. 4, 971–1055. 10.2977/prims/94Search in Google Scholar

[19] O. Y. Imanuvilov and M. Yamamoto, Global uniqueness in inverse boundary value problems for the Navier–Stokes equations and Lamé system in two dimensions, Inverse Problems 31 (2015), no. 3, Article ID 035004. 10.1088/0266-5611/31/3/035004Search in Google Scholar

[20] K. Krupchyk, M. Lassas and G. Uhlmann, Inverse boundary value problems for the perturbed polyharmonic operator, Trans. Amer. Math. Soc. 366 (2014), no. 1, 95–112. 10.1090/S0002-9947-2013-05713-3Search in Google Scholar

[21] R.-Y. Lai, Global uniqueness for an inverse problem for the magnetic Schrödinger operator, Inverse Probl. Imaging 5 (2011), no. 1, 59–73. 10.3934/ipi.2011.5.59Search in Google Scholar

[22] R.-Y. Lai, G. Uhlmann and J.-N. Wang, Inverse boundary value problem for the Stokes and the Navier–Stokes equations in the plane, Arch. Ration. Mech. Anal. 215 (2015), no. 3, 811–829. 10.1007/s00205-014-0794-1Search in Google Scholar

[23] J. M. Lee and G. Uhlmann, Determining anisotropic real-analytic conductivities by boundary measurements, Comm. Pure Appl. Math. 42 (1989), no. 8, 1097–1112. 10.1002/cpa.3160420804Search in Google Scholar

[24] A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math. (2) 143 (1996), no. 1, 71–96. 10.2307/2118653Search in Google Scholar

[25] S. K. Sahoo and M. Salo, The linearized Calderón problem for polyharmonic operators, J. Differential Equations 360 (2023), 407–451. 10.1016/j.jde.2023.03.017Search in Google Scholar

[26] J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math. (2) 125 (1987), no. 1, 153–169. 10.2307/1971291Search in Google Scholar

[27] L. Tzou, The reflection principle and Calderón problems with partial data, Math. Ann. 369 (2017), no. 1–2, 913–956. 10.1007/s00208-017-1525-3Search in Google Scholar

[28] I. N. Vekua, Generalized Analytic Functions, Pergamon Press, London, 1962. Search in Google Scholar