ON AN ANALOGUE OF THE HOLMGREN'S PROBLEM FOR 3D SINGULAR ELLIPTIC EQUATION
Juan J. NietoInstitute of Mathematics, University of Santiago de Compostela, Santiago de Compostela, 15782, SpainErkinjon KarimovDepartment of Mathematical Analysis, University of Santiago de Compostela, Santiago, 15782, Spain
ABI
Abstract
In the present paper an analogue of the Holmgren's problem for a three-dimensional elliptic equation with singular coefficients has been studied for the unique solvability. The uniqueness for the solution of considered problem is proved by an energy integral's method. Applying a method of Green's function, solution of the problem is found in an explicit form. Moreover, decomposition formulas, formulas of differentiation and some adjacent relations for Lauricella's hypergeometric functions were used to find explicit solution for aforementioned problem, which contains Appell's hypergeometric functions.
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