Boundary Value Problem for an Elliptic Equation Degenerating Inside a Domain

Abstract In this paper, we study a boundary value problem for an elliptic equation with a singular coefficient in the lower-order term that degenerates inside a domain. By applying the Hankel transform and the method of separation of variables, the solution to the Dirichlet problem is presented in explicit form. A functional relationship between the traces of the unknown function and its derivative on the line of degeneracy is obtained. The problem under study is equivalently reduced to solving a singular integral equation with a Cauchy kernel. By applying the Carleman–Vekua method, its solution is found in an explicit form.

Hali tarjima qilinmagan