REGULARIZATION OF NECESSARY CONDITIONS FOR ANONLOCAL BOUNDARY VALUE PROBLEM FOR A THREEDIMENSIONAL MIXED-TYPE EQUATION

The presented work is devoted to the study of the solution of a boundary value problem for a three-dimensional mixed-type equation with nonlocal boundary conditions in a bounded domain with a Lyapunov boundary.In the upper half-space, this is an elliptictype equation, or the Laplace equation, and in the lower half-space, it is a hyperbolic-type equation.Necessary solvability conditions are derived in both the elliptic and hyperbolic cases.Regularization of singular necessary conditions is carried out using a special scheme.The regularized relations obtained in this work are a tool for proving the Fredholm property of the problem.