Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

Emilia Blåsten; Oleg Yu. Imanuvilov; Masahiro Yamamoto

doi:10.3934/ipi.2015.9.709

Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

Emilia Blåsten^*, Oleg Yu. Imanuvilov, Masahiro Yamamoto

^*Corresponding author for this work

Not published at Aalto University

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

Abstract

We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within L-p-class of potentials with p > 2.

Original language	English
Pages (from-to)	709-723
Number of pages	15
Journal	Inverse Problems and Imaging
Volume	9
Issue number	3
DOIs	https://doi.org/10.3934/ipi.2015.9.709
Publication status	Published - Aug 2015
MoE publication type	A1 Journal article-refereed

Funding

The first author is partially supported by the ERC 2010 Advanced Grant 267700. The second author is partially supported by the NSF grant DMS 1312900. The third author partially supported by Gant-in-Aid for Scientific Research (S) 15H05740 of Japan Society for the Promotion of Science.

Keywords

Calderon problem
stability
uniqueness
GLOBAL UNIQUENESS
2 DIMENSIONS

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10.3934/ipi.2015.9.709

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@article{cff34f54152a48f68bb977625b25556f,

title = "Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials",

abstract = "We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within L-p-class of potentials with p > 2.",

keywords = "Calderon problem, stability, uniqueness, GLOBAL UNIQUENESS, 2 DIMENSIONS",

author = "Emilia Bl{\aa}sten and Imanuvilov, \{Oleg Yu.\} and Masahiro Yamamoto",

year = "2015",

month = aug,

doi = "10.3934/ipi.2015.9.709",

language = "English",

volume = "9",

pages = "709--723",

journal = "Inverse Problems and Imaging",

issn = "1930-8337",

publisher = "American Institute of Mathematical Sciences",

number = "3",

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TY - JOUR

T1 - Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

AU - Blåsten, Emilia

AU - Imanuvilov, Oleg Yu.

AU - Yamamoto, Masahiro

PY - 2015/8

Y1 - 2015/8

N2 - We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within L-p-class of potentials with p > 2.

AB - We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within L-p-class of potentials with p > 2.

KW - Calderon problem

KW - stability

KW - uniqueness

KW - GLOBAL UNIQUENESS

KW - 2 DIMENSIONS

U2 - 10.3934/ipi.2015.9.709

DO - 10.3934/ipi.2015.9.709

M3 - Article

SN - 1930-8337

VL - 9

SP - 709

EP - 723

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 3

ER -

Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

Abstract

Funding

Keywords

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