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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	095006
Journal	Inverse Problems
Volume	30
Issue number	9
DOIs	https://doi.org/10.1088/0266-5611/30/9/095006
Publication status	Published - 1 Sept 2014

Keywords

Gel'fand inverse problem
Hölder-logarithmic stability
Schrödinger equation

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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.",

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AU - Isaev, M. I.

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

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Keywords

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