Problemy Analiza — Issues of Analysis
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Probl. Anal. Issues Anal.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Problemy Analiza — Issues of Analysis, 2023, Volume 12(30), Issue 2, Pages 87–96
DOI: https://doi.org/10.15393/j3.art.2023.12230 (Mi pa377) 		 
On Cauchy problem solution for a harmonic function in a simply connected domain

E. A. Shirokova, P. N. Ivanshin

Lobachevskiy Institute of Mathematics & Mechanics, Kazan Federal University, Kremlevskaya st., 35, Kazan, 420008, Russia
Full-text PDF (2092 kB)
References:
PDF
HTML
DOI: https://doi.org/10.15393/j3.art.2023.12230
Abstract: Here we present an investigation of the Cauchy problem solvability for the Laplace equation in a simply connected plane domain. The investigation is reduced to solution of two singular integral equations. If the problem is resolvable, its solution can be restored via the integral Cauchy formula. Examples of the solvable and unsolvable problems are presented. The construction involves the auxiliary approximate conformal mapping.
Keywords: Cauchy problem, integral equation, holomorphic function, spline, approximate solution.
Received: 20.08.2022
Revised: 24.02.2023
Accepted: 23.02.2023
Document Type: Article
UDC: 517.956.223
MSC: 30-08
Language: English
Citation: E. A. Shirokova, P. N. Ivanshin, “On Cauchy problem solution for a harmonic function in a simply connected domain”, Probl. Anal. Issues Anal., 12(30):2 (2023), 87–96
Citation in format AMSBIB
\Bibitem{ShiIva23}
\by E.~A.~Shirokova, P.~N.~Ivanshin
\paper On Cauchy problem solution for a harmonic function in a simply connected domain
\jour Probl. Anal. Issues Anal.
\yr 2023
\vol 12(30)
\issue 2
\pages 87--96
\mathnet{http://mi.mathnet.ru/pa377}
\crossref{https://doi.org/10.15393/j3.art.2023.12230}
Linking options:
  • https://www.mathnet.ru/eng/pa377
  • https://www.mathnet.ru/eng/pa/v30/i2/p87
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Problemy Analiza — Issues of Analysis
    Statistics & downloads:
    Abstract page:73
    Full-text PDF :20
    References:14
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024