Studying one boundary problem for integro- differential equation with Cauchy-Riemann principal part

Many problems of mathematical physics for partial differential equations are expressed by the Laplace equation of elliptic type, which are considered mainly in the form of problems with local boundary conditions of Dirichlet, Neumann and the third type, which are supported by the entire boundary. Since, in each case, for such a second-order equation, these conditions are sufficient. However, since the Cauchy-Riemann equation is a first-order elliptic equation, the boundary value problem may not have a solution under any of the above conditions. Therefore, to overcome this contradiction, the boundary condition, which is the carrier of the entire boundary condition, is specified non locally. In this regard, this work is devoted to the study of the solution of a boundary value problem with nonlocal boundary conditions for an equation with a first-order elliptic principal part. The aim of the study was to reduce the problem to the corresponding problem for the Fredholm integral equation of the second kind.