The Dirichlet Problem for an Elliptic Equation with Singular Line Inside the Area

The paper investigates the Dirichlet problem in a rectangular domain for an elliptic equation with a singular coefficient. The bonding conditions are determined on a special line. An analogue of the Fourier method establishes the criterion of uniqueness and builds a solution in the form of a series. The substantiation of the convergence of a series in the class of regular solutions of this equation is carried out.