This article is cited in 2 papers

The solution of the basic boundary value problems for a singular elliptic equation by the method of potentials

R. M. Askhatov

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We have found fundamental solutions to a singular elliptic equation, expressed via hypergeometric functions. Using these fundamental solutions, we have built the simple and double layer potentials. We have reduced the basic boundary value problems for a singular elliptic equation to the equivalent Fredholm integral equations of the second kind and proved their solvability.

Keywords: fundamental solutions, simple and double layer potentials, boundary value problems, Fredholm integral equations, generalized shift operator.

UDC: 517.95

Received: 15.10.2013