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Exponential instability in an inverse problem for the Schrodinger equation
We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrodinger operator.We show that this problem is severely ill posed. The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are...
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2001

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Online Access:  https://hdl.handle.net/2134/680 
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author  N. Mandache 
author_facet  N. Mandache 
author_sort  N. Mandache (7160174) 
collection  Figshare 
description  We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrodinger operator.We show that this problem is severely ill posed. The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are optimal. 
format  Default Preprint 
id  rrarticle9384326 
institution  Loughborough University 
publishDate  2001 
record_format  Figshare 
spelling  rrarticle938432620010101T00:00:00Z Exponential instability in an inverse problem for the Schrodinger equation N. Mandache (7160174) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrodinger operator.We show that this problem is severely ill posed. The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are optimal. 20010101T00:00:00Z Text Preprint 2134/680 https://figshare.com/articles/preprint/Exponential_instability_in_an_inverse_problem_for_the_Schrodinger_equation/9384326 CC BYNCND 4.0 
spellingShingle  Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified N. Mandache Exponential instability in an inverse problem for the Schrodinger equation 
title  Exponential instability in an inverse problem for the Schrodinger equation 
title_full  Exponential instability in an inverse problem for the Schrodinger equation 
title_fullStr  Exponential instability in an inverse problem for the Schrodinger equation 
title_full_unstemmed  Exponential instability in an inverse problem for the Schrodinger equation 
title_short  Exponential instability in an inverse problem for the Schrodinger equation 
title_sort  exponential instability in an inverse problem for the schrodinger equation 
topic  Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified 
url  https://hdl.handle.net/2134/680 