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Volumn 8, Issue 4, 2014, Pages 1139-1150

Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map

Author keywords

Fundamental solutions; Inverse problems; Perturbation theories; Quantum mechanics; Schr dinger operator

Indexed keywords


EID: 84924995300     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2014.8.1139     Document Type: Article
Times cited : (38)

References (21)
  • 1
    • 84972834699 scopus 로고
    • Stable Determination of Conductivity by Boundary Measurements
    • G. Alessandrini, Stable Determination of Conductivity by Boundary Measurements, Appl. Anal., 27 (1988), 153-172.
    • (1988) Appl. Anal. , vol.27 , pp. 153-172
    • Alessandrini, G.1
  • 2
    • 33144457294 scopus 로고    scopus 로고
    • Stable determination of an inclusion by boundary measurements
    • G. Alessandrini and M. Di Christo, Stable determination of an inclusion by boundary measurements, SIAM J. Math. Anal., 37 (2005), 200-217.
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 200-217
    • Alessandrini, G.1    Di Christo, M.2
  • 3
    • 35348858124 scopus 로고    scopus 로고
    • Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm
    • G. Bao, S. Hou and P. Li, Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm, J. Comput. Phys., 227 (2007), 755-762.
    • (2007) J. Comput. Phys. , vol.227 , pp. 755-762
    • Bao, G.1    Hou, S.2    Li, P.3
  • 4
    • 40449100443 scopus 로고    scopus 로고
    • Recovering a potential from Cauchy data in the two-dimensional case
    • A. L. Bukhgeim, Recovering a potential from Cauchy data in the two-dimensional case, J. Inv. Ill-Posed Probl., 16 (2008), 19-33.
    • (2008) J. Inv. Ill-Posed Probl. , vol.16 , pp. 19-33
    • Bukhgeim, A.L.1
  • 5
    • 0039001417 scopus 로고    scopus 로고
    • Stability of recovery of the near-field wave from the scattering amplitude
    • I. Bushuyev, Stability of recovery of the near-field wave from the scattering amplitude, Inverse Problems, 12 (1996), 859-867.
    • (1996) Inverse Problems , vol.12 , pp. 859-867
    • Bushuyev, I.1
  • 6
    • 0030578123 scopus 로고    scopus 로고
    • A periodic Faddeev-type solution operator
    • P. Hähner, A periodic Faddeev-type solution operator, J. Diff. Equat., 128 (1996), 300-308.
    • (1996) J. Diff. Equat. , vol.128 , pp. 300-308
    • Hähner, P.1
  • 8
    • 3042528735 scopus 로고    scopus 로고
    • Increased stability in the continuation of solutions to the Helmholtz equation
    • T. Hrycak and V. Isakov, Increased stability in the continuation of solutions to the Helmholtz equation, Inverse Problems, 20 (2004), 697-712.
    • (2004) Inverse Problems , vol.20 , pp. 697-712
    • Hrycak, T.1    Isakov, V.2
  • 9
    • 84869484667 scopus 로고    scopus 로고
    • Energy and regularity dependent stability estimates for the Gelfand’s inverse problem in multi dimensions
    • M. Isaev and R. Novikov, Energy and regularity dependent stability estimates for the Gelfand’s inverse problem in multi dimensions, J. Inverse Ill-Posed Problems, 20 (2012), 313-325.
    • (2012) J. Inverse Ill-Posed Problems , vol.20 , pp. 313-325
    • Isaev, M.1    Novikov, R.2
  • 11
    • 34548693219 scopus 로고    scopus 로고
    • Increased stability in the continuation for the Helmholtz equation with variable coefficient
    • V. Isakov, Increased stability in the continuation for the Helmholtz equation with variable coefficient, Contemp. Math., AMS, 426 (2007), 255-269.
    • (2007) Contemp. Math., AMS , vol.426 , pp. 255-269
    • Isakov, V.1
  • 12
    • 80755150615 scopus 로고    scopus 로고
    • Increasing stability for the Schrödinger potential from the Dirichlet-to-Neumann map
    • V. Isakov, Increasing stability for the Schrödinger potential from the Dirichlet-to-Neumann map, Discr. Cont. Dyn. Syst.-S, 4 (2011), 631-640.
    • (2011) Discr. Cont. Dyn. Syst.-S , vol.4 , pp. 631-640
    • Isakov, V.1
  • 13
    • 84872006751 scopus 로고    scopus 로고
    • Regions of stability in the Cauchy problem for the Helmholtz equation
    • V. Isakov and S. Kindermann, Regions of stability in the Cauchy problem for the Helmholtz equation, Methods Appl. of Anal., 18 (2011), 1-29.
    • (2011) Methods Appl. Of Anal. , vol.18 , pp. 1-29
    • Isakov, V.1    Kindermann, S.2
  • 14
    • 84935878705 scopus 로고    scopus 로고
    • Increasing stability of the inverse boundary value problem for the Schrödinger equation
    • V. Isakov, S. Nagayasu, G. Uhlmann and J. N. Wang, Increasing stability of the inverse boundary value problem for the Schrödinger equation, Contemp. Math., AMS, 615 (2014), 131-143.
    • (2014) Contemp. Math., AMS , vol.615 , pp. 131-143
    • Isakov, V.1    Nagayasu, S.2    Uhlmann, G.3    Wang, J.N.4
  • 15
    • 84980073634 scopus 로고
    • Continuous dependence on data for solutions of partial differential equations with a prescribed bound
    • F. John, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551-585.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 551-585
    • John, F.1
  • 16
    • 0035473445 scopus 로고    scopus 로고
    • Exponential instability in an inverse problem for the Schrödinger equation
    • N. Mandache, Exponential instability in an inverse problem for the Schrödinger equation, Inverse Problems, 17 (2001), 1435-1444.
    • (2001) Inverse Problems , vol.17 , pp. 1435-1444
    • Mandache, N.1
  • 17
    • 84873904115 scopus 로고    scopus 로고
    • Increasing stability of the inverse boundary value problem for the acoustic equation
    • S. Nagayasu, G. Uhlmann and J. N. Wang, Increasing stability of the inverse boundary value problem for the acoustic equation, Inverse Problems, 29 (2013), 025012, 11 pp.
    • (2013) Inverse Problems , vol.29
    • Nagayasu, S.1    Uhlmann, G.2    Wang, J.N.3
  • 18
    • 21544460710 scopus 로고    scopus 로고
    • Marching schemes for inverse acoustic scattering problem
    • F. Natterer and F. Wübbeling, Marching schemes for inverse acoustic scattering problem, Numer. Math., 100 (2005), 697-710.
    • (2005) Numer. Math. , vol.100 , pp. 697-710
    • Natterer, F.1    Wübbeling, F.2
  • 19
    • 1842486610 scopus 로고    scopus 로고
    • Stability in diffraction tomography and a nonlinear “basic theorem”
    • V. Palamodov, Stability in diffraction tomography and a nonlinear “basic theorem”, J. d’ Anal. Math., 91 (2003), 247-268.
    • (2003) J. d’ Anal. Math. , vol.91 , pp. 247-268
    • Palamodov, V.1
  • 20
    • 0001110912 scopus 로고
    • Global uniqueness theorem for an inverse boundary value problem
    • J. Sylvester and G. Uhlmann, Global uniqueness theorem for an inverse boundary value problem, Ann. Math., 125 (1987), 153-169.
    • (1987) Ann. Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 21
    • 84990627147 scopus 로고
    • Inverse boundary value problems at the boundary-continuous dependence
    • J. Sylvester and G. Uhlmann, Inverse boundary value problems at the boundary-continuous dependence, Comm. Pure Appl. Math., 41 (1988), 197-221.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 197-221
    • Sylvester, J.1    Uhlmann, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.