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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, Volume 157, Book 1, Pages 5–14 (Mi uzku1288)  
Solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials

R. M. Askhatova, R. N. Abaydullinb

a Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia
b Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia
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Abstract: Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their solvability is proved.
Keywords: degenerate elliptic equation, method of potentials, double layer potential, simple layer potential, Fredholm equation, generalized translation operator.
Received: 15.12.2014
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: R. M. Askhatov, R. N. Abaydullin, “Solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 157, no. 1, Kazan University, Kazan, 2015, 5–14
Citation in format AMSBIB
\Bibitem{AskAba15}
\by R.~M.~Askhatov, R.~N.~Abaydullin
\paper Solution of the basic boundary value problems for a~degenerate elliptic equation by the method of potentials
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2015
\vol 157
\issue 1
\pages 5--14
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1288}
\elib{https://elibrary.ru/item.asp?id=23465295}
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