Effectivized Hölder-logarithmic stability estimates for the Gel'fand inverse problem

M. I. Isaev; R. G. Novikov

doi:10.1088/0266-5611/30/9/095006

Effectivized Hölder-logarithmic stability estimates for the Gel'fand inverse problem

M. I. Isaev
, R. G. Novikov

Ecole polytechnique
Moscow Institute of Physics and Technology
IEPT RAS

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We give effectivized Hölder-logarithmic energy and regularity dependent stability estimates for the Gelfand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L² and L^∞ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.

langue originale	Anglais
Numéro d'article	095006
journal	Inverse Problems
Volume	30
Numéro de publication	9
Les DOIs	https://doi.org/10.1088/0266-5611/30/9/095006
état	Publié - 1 sept. 2014

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10.1088/0266-5611/30/9/095006

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title = "Effectivized H{\"o}lder-logarithmic stability estimates for the Gel'fand inverse problem",

abstract = "We give effectivized H{\"o}lder-logarithmic energy and regularity dependent stability estimates for the Gelfand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L2 and L∞ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.",

keywords = "Gel'fand inverse problem, H{\"o}lder-logarithmic stability, Schr{\"o}dinger equation",

author = "Isaev, \{M. I.\} and Novikov, \{R. G.\}",

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AU - Novikov, R. G.

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N2 - We give effectivized Hölder-logarithmic energy and regularity dependent stability estimates for the Gelfand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L2 and L∞ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.

AB - We give effectivized Hölder-logarithmic energy and regularity dependent stability estimates for the Gelfand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L2 and L∞ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.

KW - Gel'fand inverse problem

KW - Hölder-logarithmic stability

KW - Schrödinger equation

U2 - 10.1088/0266-5611/30/9/095006

DO - 10.1088/0266-5611/30/9/095006

M3 - Article

AN - SCOPUS:84935881703

SN - 0266-5611

VL - 30

JO - Inverse Problems

JF - Inverse Problems

IS - 9

M1 - 095006

ER -

Effectivized Hölder-logarithmic stability estimates for the Gel'fand inverse problem

Résumé

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