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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

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On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle

Makhmud A. Sadybekov / Batirkhan K. Turmetov / Berikbol T. Torebek
  • Institute of Mathematics and Mathematical Modelling MES RK, Pushkin Street 125, 050010 Almaty; and Al-Farabi Kazakh National University, Al-Farabi Street 71, 050040, Almaty, Kazakhstan
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Published Online: 2015-06-04 | DOI: https://doi.org/10.1515/apam-2015-0003


The paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ2. In constructing this function we use the representation of the fundamental solution of the Laplace equation in the form of a series. An integral representation of the Green function is obtained and for some values of the parameters the Green function is given in terms of elementary functions.

Keywords: Poisson equation; Robin problem; fundamental solution; Green's function; boundary value problems

MSC: 35J08; 31A30; 31A25

About the article

Received: 2015-01-22

Revised: 2015-05-10

Accepted: 2015-05-11

Published Online: 2015-06-04

Published in Print: 2015-07-01

Funding Source: Ministry of Science and Education of the Republic of Kazakhstan

Award identifier / Grant number: 0570/GF3

Citation Information: Advances in Pure and Applied Mathematics, Volume 6, Issue 3, Pages 163–172, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2015-0003.

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