메뉴 건너뛰기




Volumn 81, Issue 2, 2013, Pages 187-258

Uniqueness for Inverse Boundary Value Problems by Dirichlet-to-Neumann Map on Subboundaries

Author keywords

complex geometric optics solution; Dirichlet to Neumann map on subboundary; elliptic operator; inverse boundary value problem; uniqueness

Indexed keywords


EID: 84888290665     PISSN: 14249286     EISSN: 14249294     Source Type: Journal    
DOI: 10.1007/s00032-013-0205-3     Document Type: Article
Times cited : (22)

References (73)
  • 2
    • 0026169803 scopus 로고
    • Identification of the Lamé coefficients from boundary observations
    • Akamatsu M., Nakamura G., Steinberg S.: Identification of the Lamé coefficients from boundary observations. Inverse Problems, 7, 335-354 (1991).
    • (1991) Inverse Problems , vol.7 , pp. 335-354
    • Akamatsu, M.1    Nakamura, G.2    Steinberg, S.3
  • 3
    • 0001666009 scopus 로고
    • solutions of elliptic equations and the determination of conductivity by boundary measurements
    • Alessandrini G.: solutions of elliptic equations and the determination of conductivity by boundary measurements. J. Diff. Equations, 84, 252-273 (1990).
    • (1990) J.Diff. Equations , vol.84 , pp. 252-273
    • Alessandrini, G.1
  • 4
    • 30444450433 scopus 로고    scopus 로고
    • Calderón's inverse conductivity problem in the plane
    • Astala K., Päivärinta L.: Calderón's inverse conductivity problem in the plane. Ann. of Math., 163, 265-299 (2006).
    • (2006) Ann. Of Math. , vol.163 , pp. 265-299
    • Astala, K.1    Päivärinta, L.2
  • 6
    • 84888287195 scopus 로고    scopus 로고
    • The inverse problem of the Shrödinger equation in the plane
    • ArXiv 1103. 6200
    • E. Blasten, The inverse problem of the Shrödinger equation in the plane. A dissection of Bukhgeim's result. ArXiv 1103. 6200.
    • A dissection of Bukhgeim's result
    • Blasten, E.1
  • 9
    • 0001659228 scopus 로고    scopus 로고
    • Uniqueness in the inverse conductivity problem with less regular conductivities
    • Brown R., Uhlmann G.: Uniqueness in the inverse conductivity problem with less regular conductivities. Comm. PDE, 22, 1009-1027 (1997).
    • (1997) Comm. PDE , vol.22 , pp. 1009-1027
    • Brown, R.1    Uhlmann, G.2
  • 10
    • 40449100443 scopus 로고    scopus 로고
    • Recovering the potential from Cauchy data in two dimensions
    • Bukhgeim A: Recovering the potential from Cauchy data in two dimensions. J. Inverse Ill-Posed Probl., 16, 19-34 (2008).
    • (2008) J. Inverse Ill-Posed Probl. , vol.16 , pp. 19-34
    • Bukhgeim, A.1
  • 11
    • 0040150838 scopus 로고
    • Uniqueness in the large of class of multidimensional inverse problems
    • Bukhgeim A., Klibanov M.: Uniqueness in the large of class of multidimensional inverse problems. Dokl. Akad. Nauk. SSSR, 260, 269-272 (1981).
    • (1981) Dokl. Akad. Nauk. SSSR , vol.260 , pp. 269-272
    • Bukhgeim, A.1    Klibanov, M.2
  • 13
    • 0002713385 scopus 로고
    • On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73
    • A. P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, 65-73, Soc. Brasil. Mat., Río de Janeiro, 1980.
    • (1980) Soc. Brasil. Mat., Río de Janeiro
    • Calderón, A.P.1
  • 14
    • 0002554964 scopus 로고
    • Sur un problème d'unicité pour les systèmes d'équations aux derivées partielles àà deux variables independentes
    • Carleman T.: Sur un problème d'unicité pour les systèmes d'équations aux derivées partielles àà deux variables independentes. Ark. Mat. Astr. Fys. 2 B, 1-9 (1939).
    • (1939) Ark. Mat. Astr. Fys. , vol.2 B , pp. 1-9
    • Carleman, T.1
  • 16
    • 9744277451 scopus 로고    scopus 로고
    • Determination of two convection coefficients from Dirichlet to Neumann map in the two-dimensional case
    • Cheng J., Yamamoto M.: Determination of two convection coefficients from Dirichlet to Neumann map in the two-dimensional case. SIAM J. Math. Anal., 35, 1371-1393 (2004).
    • (2004) SIAM J. Math. Anal. , vol.35 , pp. 1371-1393
    • Cheng, J.1    Yamamoto, M.2
  • 18
    • 0035649639 scopus 로고    scopus 로고
    • Global uniqueness in the inverse scattering problem for the Schrödinger operator with external Yang-Mills potentials
    • Eskin G.: Global uniqueness in the inverse scattering problem for the Schrödinger operator with external Yang-Mills potentials. Comm. Math. Phys., 222, 503-531 (2001).
    • (2001) Comm. Math. Phys. , vol.222 , pp. 503-531
    • Eskin, G.1
  • 19
    • 0036608345 scopus 로고    scopus 로고
    • On the inverse boundary value problem for linear isotropic elasticity
    • Eskin G., Ralston J.: On the inverse boundary value problem for linear isotropic elasticity. Inverse Problems, 18, 907-921 (2002).
    • (2002) Inverse Problems , vol.18 , pp. 907-921
    • Eskin, G.1    Ralston, J.2
  • 22
    • 79957864819 scopus 로고    scopus 로고
    • Calderón inverse problem with partial Cauchy data on Riemannian surfaces
    • Guillarmou C., Tzou L.: Calderón inverse problem with partial Cauchy data on Riemannian surfaces. Duke Math. J., 158, 83-120 (2011).
    • (2011) Duke Math. J. , vol.158 , pp. 83-120
    • Guillarmou, C.1    Tzou, L.2
  • 23
    • 84877052307 scopus 로고    scopus 로고
    • Uniqueness in Calderón's problem with Lipschitz conductivities
    • Haberman B., Tataru D.: Uniqueness in Calderón's problem with Lipschitz conductivities. Duke Math. J., 162, 497-516 (2013).
    • (2013) Duke Math. J. , vol.162 , pp. 497-516
    • Haberman, B.1    Tataru, D.2
  • 27
    • 0025550317 scopus 로고
    • Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection
    • Ikehata M.: Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection. SIAM J. Appl. Math., 50, 1635-1644 (1990).
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1635-1644
    • Ikehata, M.1
  • 28
    • 0348081503 scopus 로고
    • Boundary controllability of parabolic equations
    • Imanuvilov O.: Boundary controllability of parabolic equations. Sbornik Mathematics, 186, 879-900 (1995).
    • (1995) Sbornik Mathematics , vol.186 , pp. 879-900
    • Imanuvilov, O.1
  • 29
    • 77952047026 scopus 로고    scopus 로고
    • The Calderón problem with partial data in two dimensions
    • Imanuvilov O., Uhlmann G., Yamamoto M.: The Calderón problem with partial data in two dimensions. J. Amer. Math. Soc., 23, 655-691 (2010).
    • (2010) J. Amer. Math. Soc. , vol.23 , pp. 655-691
    • Imanuvilov, O.1    Uhlmann, G.2    Yamamoto, M.3
  • 30
    • 79551655252 scopus 로고    scopus 로고
    • Determination of second-order elliptic operators in two dimensions from partial Cauchy data
    • Imanuvilov O., Uhlmann G., Yamamoto M.: Determination of second-order elliptic operators in two dimensions from partial Cauchy data. Proc. Natl. Acad. Sci. USA, 180, 467-472 (2011).
    • (2011) Proc. Natl. Acad. Sci. USA , vol.180 , pp. 467-472
    • Imanuvilov, O.1    Uhlmann, G.2    Yamamoto, M.3
  • 31
    • 79961238224 scopus 로고    scopus 로고
    • Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets
    • Imanuvilov O., Uhlmann G., Yamamoto M: Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets. Inverse Problems, 27, 085007 (2011).
    • (2011) Inverse Problems , vol.27 , pp. 085007
    • Imanuvilov, O.1    Uhlmann, G.2    Yamamoto, M.3
  • 32
    • 84870401297 scopus 로고    scopus 로고
    • Partial Cauchy data for general second order elliptic operators in two dimensions
    • Imanuvilov O., Uhlmann G., Yamamoto M.: Partial Cauchy data for general second order elliptic operators in two dimensions. Publ. Research Institute Math. Sci., 48, 971-1055 (2012).
    • (2012) Publ. Research Institute Math. Sci. , vol.48 , pp. 971-1055
    • Imanuvilov, O.1    Uhlmann, G.2    Yamamoto, M.3
  • 33
    • 84870436092 scopus 로고    scopus 로고
    • uniqueness of Lamé coefficients from partial Cauchy data in three dimensions
    • Imanuvilov O., Uhlmann G., Yamamoto M.: uniqueness of Lamé coefficients from partial Cauchy data in three dimensions. Inverse Problems, 28, 125002 (2012).
    • (2012) Inverse Problems , vol.28 , pp. 125002
    • Imanuvilov, O.1    Uhlmann, G.2    Yamamoto, M.3
  • 35
    • 0037801616 scopus 로고    scopus 로고
    • Lipschitz stability in inverse parabolic problems by the Carleman estimate
    • Imanuvilov O., Yamamoto M.: Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Problems, 14, 1229-1245 (1998).
    • (1998) Inverse Problems , vol.14 , pp. 1229-1245
    • Imanuvilov, O.1    Yamamoto, M.2
  • 36
    • 0342902119 scopus 로고    scopus 로고
    • Global Lipschitz stability in an inverse hyperbolic problem by interior observations
    • Imanuvilov O., Yamamoto M.: Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Inverse Problems, 17, 717-728 (2001).
    • (2001) Inverse Problems , vol.17 , pp. 717-728
    • Imanuvilov, O.1    Yamamoto, M.2
  • 37
    • 0000085334 scopus 로고    scopus 로고
    • Global uniqueness and stability in determining coefficients of wave equations
    • Imanuvilov O., Yamamoto M.: Global uniqueness and stability in determining coefficients of wave equations. Comm. Partial Differential Equations, 26, 1409-1425 (2001).
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 1409-1425
    • Imanuvilov, O.1    Yamamoto, M.2
  • 38
    • 82455184323 scopus 로고    scopus 로고
    • On reconstruction of Lamé coefficients from partial Cauchy data
    • Imanuvilov O., Yamamoto M.: On reconstruction of Lamé coefficients from partial Cauchy data. J. Inverse ll-Posed Problems, 19, 881-891 (2011).
    • (2011) J. Inverse Ll-Posed Problems , vol.19 , pp. 881-891
    • Imanuvilov, O.1    Yamamoto, M.2
  • 39
    • 84866324488 scopus 로고    scopus 로고
    • Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
    • Imanuvilov O., Yamamoto M.: Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations. Inverse Problems, 28, 095015 (2012).
    • (2012) Inverse Problems , vol.28 , pp. 095015
    • Imanuvilov, O.1    Yamamoto, M.2
  • 40
    • 84861357447 scopus 로고    scopus 로고
    • Inverse boundary value problem for Schrödinger equation in two dimensions
    • Imanuvilov O., Yamamoto M.: Inverse boundary value problem for Schrödinger equation in two dimensions. SIAM J. Math. Anal., 44, 1333-1339 (2012).
    • (2012) SIAM J. Math. Anal. , vol.44 , pp. 1333-1339
    • Imanuvilov, O.1    Yamamoto, M.2
  • 41
    • 84876583567 scopus 로고    scopus 로고
    • Unique determination of potentials and semilinear terms of semilinear elliptic equations from partial Cauchy data
    • Imanuvilov O., Yamamoto M.: Unique determination of potentials and semilinear terms of semilinear elliptic equations from partial Cauchy data. J. Inverse and Ill-posed Problems, 21, 85-108 (2013).
    • (2013) J. Inverse and Ill-Posed Problems , vol.21 , pp. 85-108
    • Imanuvilov, O.1    Yamamoto, M.2
  • 43
    • 84876519941 scopus 로고    scopus 로고
    • Inverse boundary value problem for the Schrödinger equation in a cylindrical domain by partial boundary data
    • Imanuvilov O., Yamamoto M.: Inverse boundary value problem for the Schrödinger equation in a cylindrical domain by partial boundary data. Inverse Problems, 29, 045002 (2013).
    • (2013) Inverse Problems , vol.29 , pp. 045002
    • Imanuvilov, O.1    Yamamoto, M.2
  • 44
    • 84888304494 scopus 로고    scopus 로고
    • Editorial of special section on Biomedical Applications of Electrical Impedance Tomography
    • D. Isaacson, J. M̈uller, and S. Siltanen, Editorial of special section on Biomedical Applications of Electrical Impedance Tomography (pp. 391-638) in Physiological Measurement, 24 (2003).
    • (2003) Physiological Measurement , vol.24 , pp. 391-638
    • Isaacson, D.1    M̈uller, J.2    Siltanen, S.3
  • 45
    • 84908215702 scopus 로고    scopus 로고
    • On uniqueness in the inverse conductivity problem with local data
    • Isakov V.: On uniqueness in the inverse conductivity problem with local data. Inverse Problems and Imaging, 1, 95-105 (2007).
    • (2007) Inverse Problems and Imaging , vol.1 , pp. 95-105
    • Isakov, V.1
  • 46
    • 21544465323 scopus 로고    scopus 로고
    • Uniqueness of recovery of some quasiliner partial differential equations
    • Isakov V.: Uniqueness of recovery of some quasiliner partial differential equations. Comm. Partial Differential Equations, 26, 1947-1973 (2001).
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 1947-1973
    • Isakov, V.1
  • 47
    • 0035420301 scopus 로고    scopus 로고
    • Uniqueness of recovery of some systems of semiliner partial differential equations
    • Isakov V.: Uniqueness of recovery of some systems of semiliner partial differential equations. Inverse Problems, 17, 607-618 (2001).
    • (2001) Inverse Problems , vol.17 , pp. 607-618
    • Isakov, V.1
  • 48
    • 0001311566 scopus 로고
    • Global uniqueness for a two-dimensional semilinear elliptic inverse problem
    • Isakov V., Nachman A.: Global uniqueness for a two-dimensional semilinear elliptic inverse problem. Trans. AMS., 347, 3375-3390 (1995).
    • (1995) Trans. AMS. , vol.347 , pp. 3375-3390
    • Isakov, V.1    Nachman, A.2
  • 49
    • 84990587399 scopus 로고
    • Global uniqueness for a semilinear elliptic inverse problem
    • Isakov V., Sylvester J.: Global uniqueness for a semilinear elliptic inverse problem. Comm. Pure. Appl. Math., 47, 1403-1410 (1994).
    • (1994) Comm. Pure. Appl. Math. , vol.47 , pp. 1403-1410
    • Isakov, V.1    Sylvester, J.2
  • 50
    • 0035421328 scopus 로고    scopus 로고
    • resistance tomography to detect leaks from buried pipes
    • Jordana J., Gasulla M., Pallààs-Areny R.: resistance tomography to detect leaks from buried pipes. Meas. Sci. Technol., 12, 1061-1068 (2001).
    • (2001) Meas. Sci. Technol. , vol.12 , pp. 1061-1068
    • Jordana, J.1    Gasulla, M.2    Pallààs-Areny, R.3
  • 51
    • 0036685542 scopus 로고    scopus 로고
    • Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map
    • Kang H., Nakamura G.: Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map. Inverse Problems, 18, 1079-1088 (2002).
    • (2002) Inverse Problems , vol.18 , pp. 1079-1088
    • Kang, H.1    Nakamura, G.2
  • 54
    • 34547164277 scopus 로고    scopus 로고
    • The Calderón problem with partial data
    • Kenig C., Sjöstrand J., Uhlmann G.: The Calderón problem with partial data. Ann. of Math., 165, 567-591 (2007).
    • (2007) Ann. Of Math. , vol.165 , pp. 567-591
    • Kenig, C.1    Sjöstrand, J.2    Uhlmann, G.3
  • 55
    • 30444459486 scopus 로고    scopus 로고
    • The Calderón problem with partial data for less smooth conductivities
    • Knudsen K.: The Calderón problem with partial data for less smooth conductivities. Comm. Partial Differential Equations, 31, 57-71 (2006).
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 57-71
    • Knudsen, K.1
  • 56
    • 0021580594 scopus 로고
    • Identification of an unknown conductivity by means of measurements at the boundary, in Inverse Problems
    • Kohn R., Vogelius M.: Identification of an unknown conductivity by means of measurements at the boundary, in Inverse Problems. edited by D. McLaughlin, SIAM-AMS Proceedings, 14, 113-123 (1984).
    • (1984) Edited by D. McLaughlin, SIAM-AMS Proceedings , vol.14 , pp. 113-123
    • Kohn, R.1    Vogelius, M.2
  • 58
    • 0030550779 scopus 로고    scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • Nachman A.: Global uniqueness for a two-dimensional inverse boundary value problem. Ann. of Math., 143, 71-96 (1996).
    • (1996) Ann. Of Math. , vol.143 , pp. 71-96
    • Nachman, A.1
  • 59
    • 0000107961 scopus 로고
    • Identification of Lamé parameters by boundary measurements
    • Nakamura G., Uhlmann G.: Identification of Lamé parameters by boundary measurements. American Journal of Mathematics, 115, 1161-1187 (1993).
    • (1993) American Journal of Mathematics , vol.115 , pp. 1161-1187
    • Nakamura, G.1    Uhlmann, G.2
  • 60
    • 0000135170 scopus 로고
    • Global uniqueness for an inverse boundary value problem arising in elasticity
    • ERRATUM, Invent. Math., 152(2003), 205-207
    • G. Nakamura, G. Uhlmann, Global uniqueness for an inverse boundary value problem arising in elasticity, Invent. Math., 118 (1994), 457-474, ERRATUM, Invent. Math., 152(2003), 205-207.
    • (1994) Invent. Math. , vol.118 , pp. 457-474
    • Nakamura, G.1    Uhlmann, G.2
  • 61
    • 21844496162 scopus 로고
    • Inverse boundary problems at the boundary for an elastic system
    • Nakamura G., Uhlmann G.: Inverse boundary problems at the boundary for an elastic system. SIAM J. Math. Anal., 26, 263-279 (1995).
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 263-279
    • Nakamura, G.1    Uhlmann, G.2
  • 62
    • 78651369747 scopus 로고    scopus 로고
    • New global stability estimates for the Gel'fand-Calderon inverse problem
    • Novikov R. G.: New global stability estimates for the Gel'fand-Calderon inverse problem. Inverse problems, 27, 015001 (2011).
    • (2011) Inverse Problems , vol.27 , pp. 015001
    • Novikov, R.G.1
  • 63
    • 79959865188 scopus 로고    scopus 로고
    • Global uniqueness and reconstruction for the multichannel Gel'fand-Calderón inverse problem in two dimensions
    • Novikov R. G., Santacesaria M: Global uniqueness and reconstruction for the multichannel Gel'fand-Calderón inverse problem in two dimensions. Bull. Sci. Math., 135, 421-434 (2011).
    • (2011) Bull. Sci. Math. , vol.135 , pp. 421-434
    • Novikov, R.G.1    Santacesaria, M.2
  • 67
    • 84968484652 scopus 로고
    • An inverse boundary value problem for the Schrödinger operator with vector potential
    • Z. Sun, An inverse boundary value problem for the Schrödinger operator with vector potential, Trans. Amer. Math. Soc., 338 (1993), 953-969.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 953-969
    • Sun, Z.1
  • 68
    • 0000087330 scopus 로고    scopus 로고
    • On a quasilinear inverse boundary value problem
    • Z. Sun, On a quasilinear inverse boundary value problem, Math. Z., 221 (1996), 293-307.
    • (1996) Math. Z. , vol.221 , pp. 293-307
    • Sun, Z.1
  • 69
    • 84990586454 scopus 로고
    • An anisotropic inverse boundary value problem
    • J. Sylvester, An anisotropic inverse boundary value problem, Comm. Pure Appl. Math., 43 (1990), 201-232.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 201-232
    • Sylvester, J.1
  • 70
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153-169.
    • (1987) Ann. of Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.