Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation

Details Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation

2012-04-23

arxiv.org/abs/1204.5026v1

Mathematics

Analysis of PDEs

12 pages, 1 figure

Scientific paper

The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have been used. Since, found Green's function contains a hypergeometric function of Appell, we had to deal with decomposition formulas, formulas of differentiation and some adjacent relations for this hypergeometric function in order to get explicit solution of the formulated problem.

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