Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 7
58
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Stability for the inverse potential problem by the local Dirichlet-to-Neumann map for the Schrödinger equation

Pages 899-914 | Received 09 May 2006, Accepted 07 Jun 2007, Published online: 27 Sep 2007

References

  • Alessandrini , G . 1988 . Stable determination of conductivity by boundary measerements . Applicable Analysis , 27 : 153 – 72 .
  • Ammari , H and Uhlmann , G . 2004 . Reconstruction of the potential from partial cauchy data for the Schrödinger equation . Indiana University Mathematics Journal , 531 : 169 – 183 .
  • Bardos , G , Lebeau , J and Rauch , C . 1992 . Sharp sufficient conditions for the obsevation, control and stabilisation from the boundary . SIAM Journal of Control and Optimization , 30 : 1024 – 165 .
  • Bellassoued , M . 2004, . Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation. . Inverse Problems , 20 : 1033 – 1052 .
  • Brown , RM and Uhlmann , GA . 1997 . Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions . Communications in Partial Differntial Equations , 22 : 1009 – 1027 .
  • Bukhgeim , AL and Uhlmann , G . 2002 . Recovering a potential from partial Cauchy data . Communications in Partial Differntial Equations , 27 : 653 – 668 .
  • Calderon , AP . 1980 . On an inverse boundary value problem.Seminar on Numerical Analysis and its Applications to Continuum Physics . (Rio de Janeiro: Soc. Brasileira de Matematica) , : 65 – 73 .
  • Cheng , J and Nakamura , G . 2001 . Stability for the inverse potential problem by finite measurements on the boundary . Inverse Problems , 17 : 273 – 280 .
  • Heck , H and .and Wang , J.N . 2006 . Stability estimates for the inverse boundary value problem by partial Cauchy data . Inverse Problems , 22 : 1787 – 1796 .
  • Isakov , V . 1998 . Inverse Problems for Partial Differential Equations , Berlin : Springer .
  • Kenig , CE , Uhlmann , G and Sjöstrand , J . 2007 . The Calderón problem with partial data . Annals of Mathematics , 165 ( 2 ) : 567 – 591 .
  • Kohn , R and Vogelius , M . 1984 . Determining conductivity by boundary measurements . I.Communications on Pure and Applied Mathematics , 37 : 289 – 298 . Kohn, R.and Vogelius, M., 1985, Determining conductivity by boundary measerements, II.Communications on Pure and Applied Mathematics38643--667
  • Lebeau , G and Robbiano , L . 1995 . Controle exact de l'équation de la chaleur . Communications in Partial Differntial Equations , 20 : 335 – 356 .
  • Lebeau , G and Robbiano , L . 1997 . Stabilisation de l'équation des ondes par le bord . Duke Mathematical Journal , 86 : 465 – 491 .
  • Lions , JL and Magenes , E . 1972 . Non-homogeneous Boundary Value Problems and Applications , Vol. 4 , 1 – 2 . Berlin : Springer .
  • Magnanini , R and Papi , G . 1985 . An inverse problem for the Helmoholtz equation . Inverse problems , 1 : 357 – 370 .
  • Mandache , N . 2001 . Exponential instability in an inverse problem for the Schrödinger equation . Inverse Problems , 17 : 1435 – 1444 .
  • Nachman , AI . 1985 . Global uniqueness for a two-dimensional inverse boundary value problem . Annals of Mathematics , 14 ( 2 ) : 71 – 96 .
  • Nakamura , G , Sun , Z and Uhlmann , G . 1995 . Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field . Mathematische Annalen , 30 ( 3 ) : 377 – 388 .
  • Payne , LE . 1975 . Improperly Posed Problems in Partial Differential Equations , Philadelphia : S.I.A.M .
  • Sylvester , J and Uhlmann , G. 1987 . A global uniqueness theorem for an inverse boundary value problem . Annuals of Mathematics , 12 ( 5 ) : 153 – 169 .
  • Sylvester , J and Uhlmann , G . 1988 . Inverse boundary value problems at the boundary-continuous dependence . Communications on Pure and Applied Mathematics ,

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.