The Dirichlet problem for a 3D elliptic equation with two singular coefficients

作者：Karimov E T^*; Nieto J J

来源：Computers & Mathematics with Applications, 2011, 62(1): 214-224.

DOI：10.1016/j.camwa.2011.04.068

• Dirichlet problem
• 3D elliptic equation with singular coefficients
• Green's function
• Gauss and Appell's hypergeometric functions

In the present work, we investigate the Dirichlet problem for a three-dimensional (3D) elliptic equation with two singular coefficients. We find four fundamental solutions of the equation, containing hypergeometric functions of Appel!. Then using an "a-b-c" method, the uniqueness for the solution of the Dirichlet problem is proved. Applying a method of Green's function, we are able to find the solution of the problem in an explicit form. Moreover, decomposition formulas, formulas of differentiation and some adjacent relations for Appell's hypergeometric functions were used in order to find the explicit solution for the formulated problem.

• 出版日期2011-7