A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain

T. G. Ergashev ; Z. R. Tulakova

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 58-72.

Résumé

Solutions of the Dirichlet and Neumann problems for multidimensional singular elliptic equations in an infinite domain were 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. In proving the existence of a unique solution to the problem posed, representation of the multiple Lauricella hypergeometric function at limiting values of the variables and a new formula for multiple improper integrals, which generalizes the well-known formula from the handbook of I.S. Gradshtein and I.M. Ryzhik, are used.

Détail

Keywords: Problem with mixed boundary conditions in an infinite domain, multidimensional elliptic equation with singular coefficients, fundamental solution, formula for the limit values of a hypergeometric function, Lauricella hypergeometric function of several variables.

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