A Problem with Mixed Boundary Conditions for a Singular Elliptic Equation in an Infinite Domain

Solutions of the Dirichlet and Neumann problems for multidimensional singular elliptic equations in an infinite domain can be found in explicit forms in recent works of the authors. In this paper, a problem with mixed conditions, which is a natural generalization of the previously considered Dirichlet and Neumann problems, is studied. To prove the existence of a unique solution to the problem, we use the representation of the multiple Lauricella hypergeometric function at limiting values of the variables and a new representation for multiple improper integrals which generalizes the well-known representation from the handbook of Gradshtein and Ryzhik.

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