Inverse boundary-value problems of cauchy type for harmonic functions

We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generaliz...

Full description

Saved in:
Bibliographic Details
Published in:Russian mathematics Vol. 56; no. 12; pp. 71 - 75
Main Authors: Abubakirov, N. R., Aksent’ev, L. A.
Format: Journal Article
Language:English
Published: Heidelberg Allerton Press, Inc 01.12.2012
Subjects:
ISSN:1066-369X, 1934-810X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generalize the obtained results for the case of doubly connected domains.
AbstractList We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generalize the obtained results for the case of doubly connected domains.
Author Aksent’ev, L. A.
Abubakirov, N. R.
Author_xml – sequence: 1
  givenname: N. R.
  surname: Abubakirov
  fullname: Abubakirov, N. R.
  email: Nail.Abubakirov@ksu.ru
  organization: Kazan (Volga Region) Federal University
– sequence: 2
  givenname: L. A.
  surname: Aksent’ev
  fullname: Aksent’ev, L. A.
  organization: Kazan (Volga Region) Federal University
BookMark eNp9kEFrAjEQhUOxULX9Ab3lD2w7k8SsORaxrSD00Ba8LdnZpK5oIokr-O-7ordCT2_gzfd4vBEbhBgcY48ITxJBPn8iaC21WaFAATCFGzZEI1UxRVgN-ru3i7N_x0Y5bwAmWig9ZPNFOLqUHa9jFxqbTsXRbjvH9ynWW7fLPHpOtqP1iR9Oe8d9THxt0y6GlrjvAh3aGPI9u_V2m93DVcfs-3X-NXsvlh9vi9nLsiCh4FBo2zQ0RaptCajKWnorjKSJ0aUhr1E3QjYOQQktJgZrTcIZRUJYowA1yTHDSy6lmHNyvtqndte3rhCq8w7Vnx16RlyY3P-GH5eqTexS6Gv-A_0CxEBhsA
Cites_doi 10.4213/mzm8553
ContentType Journal Article
Copyright Allerton Press, Inc. 2012
Copyright_xml – notice: Allerton Press, Inc. 2012
DBID AAYXX
CITATION
DOI 10.3103/S1066369X12120080
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1934-810X
EndPage 75
ExternalDocumentID 10_3103_S1066369X12120080
GroupedDBID -5D
-5G
-BR
-EM
-Y2
-~C
.86
.VR
06D
0R~
0VY
123
1N0
29P
2J2
2JN
2JY
2KG
2LR
2~H
30V
4.4
408
40D
40E
5VS
6NX
78A
8UJ
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABMNI
ABMQK
ABNWP
ABQBU
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACAOD
ACBXY
ACCUX
ACDTI
ACGFS
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACZOJ
ADHHG
ADHIR
ADINQ
ADKNI
ADRFC
ADURQ
ADYFF
ADZKW
AEBTG
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AEOHA
AEPYU
AETLH
AEVLU
AEXYK
AFGCZ
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHSBF
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARMRJ
AXYYD
B-.
BA0
BAPOH
BDATZ
BGNMA
CAG
COF
CS3
DDRTE
DNIVK
DPUIP
EBLON
EBS
EIOEI
EJD
ESBYG
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
H13
HF~
HG6
HLICF
HMJXF
HRMNR
HZ~
IJ-
IKXTQ
IWAJR
I~X
I~Z
J-C
JBSCW
JZLTJ
KOV
LLZTM
M4Y
MA-
NB0
NPVJJ
NQJWS
NU0
O9-
O93
O9J
P9R
PF0
PT4
QOS
R89
R9I
RIG
RNS
ROL
RPX
RSV
S16
S1Z
S27
S3B
SAP
SDH
SHX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
TSG
TUC
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W48
WK8
XU3
YLTOR
ZMTXR
~A9
AAPKM
AAYXX
ABDBE
ABFSG
ABJCF
ABRTQ
ACSTC
AEZWR
AFDZB
AFFHD
AFHIU
AFKRA
AFOHR
AHPBZ
AHWEU
AIXLP
ATHPR
AZQEC
BENPR
BGLVJ
CCPQU
CITATION
DWQXO
GNUQQ
HCIFZ
M2P
M7S
PHGZM
PHGZT
PQGLB
PTHSS
ID FETCH-LOGICAL-c240t-6addc81cba70147b3fa293c59679cf616d23de104262591b6c2e94c22a94016c3
IEDL.DBID RSV
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000439486500008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1066-369X
IngestDate Sat Nov 29 05:49:34 EST 2025
Fri Feb 21 02:34:23 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 12
Keywords inverse boundary-value problems
boundary-value problems for analytic functions
harmonic functions
Cauchy problem
Language English
License http://www.springer.com/tdm
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c240t-6addc81cba70147b3fa293c59679cf616d23de104262591b6c2e94c22a94016c3
PageCount 5
ParticipantIDs crossref_primary_10_3103_S1066369X12120080
springer_journals_10_3103_S1066369X12120080
PublicationCentury 2000
PublicationDate 20121200
2012-12-00
PublicationDateYYYYMMDD 2012-12-01
PublicationDate_xml – month: 12
  year: 2012
  text: 20121200
PublicationDecade 2010
PublicationPlace Heidelberg
PublicationPlace_xml – name: Heidelberg
PublicationTitle Russian mathematics
PublicationTitleAbbrev Russ Math
PublicationYear 2012
Publisher Allerton Press, Inc
Publisher_xml – name: Allerton Press, Inc
References Demtchenko (CR2) 1929; 189
Gahov (CR5) 1977
Tumashev, Nuzhin (CR3) 1965
Demidov, Platushchikhin (CR1) 2010; 87
Petrovskii (CR4) 1961
G. G. Tumashev (9444_CR3) 1965
I. A. Petrovskii (9444_CR4) 1961
F. D. Gahov (9444_CR5) 1977
B. Demtchenko (9444_CR2) 1929; 189
A. S. Demidov (9444_CR1) 2010; 87
References_xml – volume: 189
  start-page: 725
  year: 1929
  end-page: 726
  ident: CR2
  article-title: Sur un Probleme Inverse au Probleme de Dirichlet
  publication-title: Compt. Rend. Acad. Sci. Paris
– volume: 87
  start-page: 141
  issue: 1
  year: 2010
  end-page: 143
  ident: CR1
  article-title: Explicit Formula for the Gradient of a Harmonic Function from Its Analytic Cauchy Data on the Analytic Curve
  publication-title: Matem. Zametki
  doi: 10.4213/mzm8553
– year: 1961
  ident: CR4
  publication-title: Lectures on Partial Differential Equations
– year: 1965
  ident: CR3
  publication-title: Inverse Boundary-Value Problems with Applications
– year: 1977
  ident: CR5
  publication-title: Boundary-Value Problems
– volume: 87
  start-page: 141
  issue: 1
  year: 2010
  ident: 9444_CR1
  publication-title: Matem. Zametki
  doi: 10.4213/mzm8553
– volume-title: Inverse Boundary-Value Problems with Applications
  year: 1965
  ident: 9444_CR3
– volume: 189
  start-page: 725
  year: 1929
  ident: 9444_CR2
  publication-title: Compt. Rend. Acad. Sci. Paris
– volume-title: Boundary-Value Problems
  year: 1977
  ident: 9444_CR5
– volume-title: Lectures on Partial Differential Equations
  year: 1961
  ident: 9444_CR4
SSID ssj0056246
Score 1.832045
Snippet We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown...
SourceID crossref
springer
SourceType Index Database
Publisher
StartPage 71
SubjectTerms Brief Communications
Mathematics
Mathematics and Statistics
Title Inverse boundary-value problems of cauchy type for harmonic functions
URI https://link.springer.com/article/10.3103/S1066369X12120080
Volume 56
WOSCitedRecordID wos000439486500008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAVX
  databaseName: SpringerLINK Contemporary 1997-Present
  customDbUrl:
  eissn: 1934-810X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0056246
  issn: 1066-369X
  databaseCode: RSV
  dateStart: 20070101
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV09T8MwED1BYYCBb0T5kgcmkEXsOE48ItSKASpEoeoW2a4tWFKUtEj999hOglQBA-ynKDqd773znd8BXHDrZd5iPxRGBGYmYVixlOJIZkKJSFId5JpG9-lgkI3H4rF5x1210-5tSzJk6lBXRvH1kHh05GJMXLb1RGcV1hzaZf40Pg1Hbfp1eF4_KXLW2JvXrcyfP7EMRsud0AAw_e1__doObDV8Et3UAbALK6bYg82HLzHWah96XkujrAxSYYVSucBe4dugZpdMhaYWaTnXrwvkL2SRo7HIC1p70VzkcS-E5gG89HvPt3e42Z6AtUPpGeYuc-mMaCVTVwalKrbSQbtOBE-FtpzwCY0nhgRJ-kQQxTU1gmlKpXA1F9fxIXSKaWGOAFlhuRXSJlxLpiIqJhGTmtHUsS1FVdSFy9aN-XstkpG74sL7Jv_mmy5ctU7Mm_NS_W59_CfrE9hwhIbW4yan0JmVc3MG6_pj9laV5yFOPgFlQbVT
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NSwMxEB20CurBb7F-5uBJCe5ms9nmKNJSsS1ia-ltSdIEvbSy2wr99ybZXaGoB70PSxgm897sTN4AXDHjZN4iNxQWckx1TLGkCcGBaHDJA0GUl2sadpJerzEa8afyHXdeTbtXLUmfqX1dGUS3_dChI-Oj0GZbR3RWYY1awHJzfM_9YZV-LZ4XT4qsNXbmRSvz508sg9FyJ9QDTGvnX0fbhe2ST6K7IgD2YEVP9mGr-yXGmh9A02lpZLlG0q9QyhbYKXxrVO6SydHUICXm6nWB3A9ZZGkscoLWTjQXOdzzoXkIL63m4L6Ny-0JWFmUnmFmM5dqhEqKxJZBiYyMsNCuYs4SrgwL2ZhEYx16SfqYh5IpojlVhAhuay6moiOoTaYTfQzIcMMMFyZmSlAZED4OqFCUJJZtSSKDOlxXbkzfC5GM1BYXzjfpN9_U4aZyYlrel_x365M_WV_CRnvQ7aSdh97jKWxackOK0ZMzqM2yuT6HdfUxe8uzCx8zn_C2uDc
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEB60iujBt1ifOXhSQnez2WxzFG1RrKVQLb0tSZqgl23Z3Qr99yb7EIp6EO_DEobJfDM7k-8DuGLG0bwFbinM55jqkGJJI4I90eaSe4Kogq5p1Iv6_fZ4zAeVzmlWb7vXI8nyTYNjaUry1mxiWkWP6QWtoe-QkvGxbzOvK3pWYY06zSDXrg9HdSq22F4-L7LW2JmXY82fP7EMTMtT0QJsujv_PuYubFd1JrotA2MPVnSyD1vPXySt2QF0HMdGmmkkC2mldIEd87dGlcZMhqYGKTFXbwvkftQiW94iR3TtyHSRw8MiZA_htdt5uXvAlaoCVha9c8xsRlNtX0kR2fYokoERFvJVyFnElWE-m5Bgov2Cqj7kvmSKaE4VIYLbXoyp4AgayTTRx4AMN8xwYUKmBJUe4ROPCkVJZKswSaTXhOvapfGsJM-IbdPhfBN_800TbmqHxtU9yn63PvmT9SVsDO67ce-x_3QKm7bmIeVGyhk08nSuz2FdfeTvWXpRhM8nSa_BGw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Inverse+boundary-value+problems+of+cauchy+type+for+harmonic+functions&rft.jtitle=Russian+mathematics&rft.au=Abubakirov%2C+N.+R.&rft.au=Aksent%E2%80%99ev%2C+L.+A.&rft.date=2012-12-01&rft.pub=Allerton+Press%2C+Inc&rft.issn=1066-369X&rft.eissn=1934-810X&rft.volume=56&rft.issue=12&rft.spage=71&rft.epage=75&rft_id=info:doi/10.3103%2FS1066369X12120080&rft.externalDocID=10_3103_S1066369X12120080
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1066-369X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1066-369X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1066-369X&client=summon