메뉴 건너뛰기




Volumn 5, Issue 2, 2011, Pages 297-322

On an inverse problem in electromagnetism with local data: Stability and uniqueness

Author keywords

Electromagnetism; Inverse boundary value problem

Indexed keywords


EID: 79957932121     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2011.5.297     Document Type: Article
Times cited : (27)

References (30)
  • 1
    • 84972834699 scopus 로고
    • Stable determination of the conductivity by boundary measurements
    • G. Alessandrini, Stable determination of the conductivity by boundary measurements, Appl. Anal., 27 (1988), 153-172.
    • (1988) Appl. Anal. , vol.27 , pp. 153-172
    • Alessandrini, G.1
  • 2
    • 21844471512 scopus 로고    scopus 로고
    • Lipschitz stability for the inverse conductivity problem
    • G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Adv. Appl. Math., 35 (2005) 207-241.
    • (2005) Adv. Appl. Math. , vol.35 , pp. 207-241
    • Alessandrini, G.1    Vessella, S.2
  • 3
    • 17444429256 scopus 로고    scopus 로고
    • Calderón's inverse problem for anisotropic conduc- tivity in the plane
    • K. Astala, L. Päivärinta and M. Lassas, Calderón's inverse problem for anisotropic conduc- tivity in the plane, Comm. PDE, 30 (2005), 207-224.
    • (2005) Comm. PDE. , vol.30 , pp. 207-224
    • Astala, K.1    Päivärinta, L.2    Lassas, M.3
  • 4
    • 0030548099 scopus 로고    scopus 로고
    • Global uniqueness in the impedance imaging problem for less regular conductivities
    • R. Brown, Global uniqueness in the impedance imaging problem for less regular conductivities, SIAM J. Math. Anal., 27 (1996), 1049-1056.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1049-1056
    • Brown, R.1
  • 5
    • 0036381894 scopus 로고    scopus 로고
    • Recovering a potential from partial Cauchy data
    • A. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, Comm. PDE, 27 (2002), 653-668.
    • (2002) Comm. PDE. , vol.27 , pp. 653-668
    • Bukhgeim, A.1    Uhlmann, G.2
  • 6
    • 74949143869 scopus 로고    scopus 로고
    • Inverse boundary value problem for Maxwell equations with local data
    • P. Caro, P. Ola and M. Salo, Inverse boundary value problem for Maxwell equations with local data, Comm. PDE, 34 (2009), 1425-1464.
    • (2009) Comm. PDE. , vol.34 , pp. 1425-1464
    • Caro, P.1    Ola, P.2    Salo, M.3
  • 7
    • 78049447856 scopus 로고    scopus 로고
    • Stable determination of the electromagnetic coecients by boundary measurements
    • 105014
    • P. Caro, Stable determination of the electromagnetic coecients by boundary measurements, Inverse Problems, 26 (2010), 105014, 25 pp.
    • (2010) Inverse Problems , vol.26 , pp. 25
    • Caro, P.1
  • 8
    • 0002283266 scopus 로고
    • The uniqueness of a solution to an inverse scattering problem for electromagnetic waves
    • D. Colton and L. Päivärinta, The uniqueness of a solution to an inverse scattering problem for electromagnetic waves, Arch. Rational Mech. Anal., 119 (1992), 59-70.
    • (1992) Arch. Rational Mech. Anal. , vol.119 , pp. 59-70
    • Colton, D.1    Päivärinta, L.2
  • 9
    • 33749015207 scopus 로고    scopus 로고
    • Stability estimates for the inverse boundary value problem by partial Cauchy data
    • H. Heck and J.-N. Wang, Stability estimates for the inverse boundary value problem by partial Cauchy data, Inverse Problems, 22 (2006), 1787-1796.
    • (2006) Inverse Problems , vol.22 , pp. 1787-1796
    • Heck, H.1    Wang, J.-N.2
  • 11
    • 33645037724 scopus 로고    scopus 로고
    • Carleman estimates and applications to inverse problems
    • V. Isakov, Carleman estimates and applications to inverse problems, Milan J. Math., 72 (2004), 249-271.
    • (2004) Milan J. Math. , vol.72 , pp. 249-271
    • Isakov, V.1
  • 12
    • 84908215702 scopus 로고    scopus 로고
    • On uniqueness in the inverse conductivity problem with local data
    • V. Isakov, On uniqueness in the inverse conductivity problem with local data, Inverse Probl. Imaging, 1 (2007), 95-105.
    • (2007) Inverse Probl. Imaging. , vol.1 , pp. 95-105
    • Isakov, V.1
  • 13
    • 0000271720 scopus 로고
    • The inhomogeneous Dirichlet problem in Lipschitz domains
    • D. Jerison and C. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains, J. Funct. Anal., 130 (1995), 161-219.
    • (1995) J. Funct. Anal. , vol.130 , pp. 161-219
    • Jerison, D.1    Kenig, C.2
  • 14
    • 0038002659 scopus 로고    scopus 로고
    • Total determination of material parameters from electromagnetic boundary information
    • M. Joshi, S. R. McDowall, Total determination of material parameters from electromagnetic boundary information, Pacific J. Math., 193 (2000), 107-129.
    • (2000) Pacific J. Math. , vol.193 , pp. 107-129
    • Joshi, M.1    McDowall, S.R.2
  • 15
    • 79953165786 scopus 로고    scopus 로고
    • Inverse problems for the anisotropic Maxwell equations
    • C. E. Kenig, M. Salo and G. Uhlmann, Inverse problems for the anisotropic Maxwell equations, Duke Math. J., 157 (2011), 369-419.
    • (2011) Duke Math. J. , vol.157 , pp. 369-419
    • Kenig, C.E.1    Salo, M.2    Uhlmann, G.3
  • 16
    • 34547164277 scopus 로고    scopus 로고
    • The Calderón problem with partial data
    • C. E. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data, Ann. of Math., 165 (2007), 567-591.
    • (2007) Ann. of Math. , vol.165 , pp. 567-591
    • Kenig, C.E.1    Sjöstrand, J.2    Uhlmann, G.3
  • 17
    • 33748439229 scopus 로고    scopus 로고
    • Maxwell's equations with a polarization independent wave velocity: Direct and inverse problems
    • Y. Kurylev, M. Lassas, Matti and E. Somersalo, Maxwell's equations with a polarization independent wave velocity: Direct and inverse problems, J. Math. Pures Appl., 86 (2006), 237-270.
    • (2006) J. Math. Pures Appl. , vol.86 , pp. 237-270
    • Kurylev, Y.1    Lassas, M.2    Matti3    Somersalo, E.4
  • 19
    • 36749007385 scopus 로고    scopus 로고
    • Re ection principle for the Maxwell equations and its application to inverse electromagnetic scattering
    • H. Liu, M. Yamamoto and J. Zou, Re ection principle for the Maxwell equations and its application to inverse electromagnetic scattering, Inverse Problems, 23 (2007), 2357-2366.
    • (2007) Inverse Problems , vol.23 , pp. 2357-2366
    • Liu, H.1    Yamamoto, M.2    Zou, J.3
  • 20
    • 23044520864 scopus 로고    scopus 로고
    • An electromagnetic inverse problem in chiral media
    • S. R. McDowall, An electromagnetic inverse problem in chiral media, Trans. Amer. Math. Soc., 352 (2000), 2993-3013.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 2993-3013
    • McDowall, S.R.1
  • 21
    • 11144332000 scopus 로고    scopus 로고
    • Sharp Hodge decomposition, Maxwell's equations, and vector Poisson problems on non-smooth, three-dimensional riemannian manifolds
    • M. Mitrea, Sharp Hodge decomposition, Maxwell's equations, and vector Poisson problems on non-smooth, three-dimensional riemannian manifolds, Duke Math. J., 125 (2004), 467-547.
    • (2004) Duke Math. J. , vol.125 , pp. 467-547
    • Mitrea, M.1
  • 22
    • 84973999369 scopus 로고
    • An inverse boundary value problem in electrodynamics
    • P. Ola, L. Päivärinta and E. Somersalo, An inverse boundary value problem in electrodynamics, Duke Math. J., 70 (1993), 617-653.
    • (1993) Duke Math. J. , vol.70 , pp. 617-653
    • Ola, P.1    Päivärinta, L.2    Somersalo, E.3
  • 23
    • 78049421023 scopus 로고    scopus 로고
    • Inverse problems for time harmonic electrodynamics. Inside out: Inverse problems and applications
    • Cambridge Univ. Press, Cambridge
    • P. Ola, L. Päivärinta and E. Somersalo, Inverse problems for time harmonic electrodynamics. Inside out: inverse problems and applications, 169-191, Math. Sci. Res. Inst. Publ., 47, Cambridge Univ. Press, Cambridge, 2003.
    • (2003) Math. Sci. Res. Inst. Publ. , vol.47 , pp. 169-191
    • Ola, P.1    Päivärinta, L.2    Somersalo, E.3
  • 24
    • 0030216087 scopus 로고    scopus 로고
    • Electromagnetic inverse problems and generalized Sommerfeld potentials
    • P. Ola and E. Somersalo, Electromagnetic inverse problems and generalized Sommerfeld potentials, SIAM J. Appl. Math., 56 (1996), 1129-1145.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1129-1145
    • Ola, P.1    Somersalo, E.2
  • 25
    • 70349623269 scopus 로고    scopus 로고
    • Carleman estimates and inverse problems for Dirac operators
    • M. Salo and L. Tzou, Carleman estimates and inverse problems for Dirac operators, Math. Ann., 344 (2009), 161-184.
    • (2009) Math. Ann. , vol.344 , pp. 161-184
    • Salo, M.1    Tzou, L.2
  • 26
    • 77954302801 scopus 로고    scopus 로고
    • Inverse problems with partial data for a Dirac system: A Carleman estimate approach
    • M. Salo and L. Tzou, Inverse problems with partial data for a Dirac system: A Carleman estimate approach, Adv. Math., 225 (2010), 487-513.
    • (2010) Adv. Math. , vol.225 , pp. 487-513
    • Salo, M.1    Tzou, L.2
  • 27
    • 38249007884 scopus 로고
    • A linearized inverse boundary value problem for Maxwell's equations
    • E. Somersalo, D. Isaacson and M. Cheney, A linearized inverse boundary value problem for Maxwell's equations, J. Comp. Appl. Math., 42 (1992), 123-136.
    • (1992) J. Comp. Appl. Math. , vol.42 , pp. 123-136
    • Somersalo, E.1    Isaacson, D.2    Cheney, M.3
  • 29
    • 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
  • 30
    • 0042420166 scopus 로고    scopus 로고
    • Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers
    • H. Triebel, Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers, Rev. Mat. Complut., 15 (2002), 475-524.
    • (2002) Rev. Mat. Complut. , vol.15 , pp. 475-524
    • Triebel, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.