INVESTIGATING THE SOLUTION OF A BOUNDARY PROBLEM

Abstract

For the elliptic type equation of the first form, the solution of the boundary problem in different regions was investigated. Here, the solution of a boundary value problem in the half-plane for the Cauchy-Riemann equation is investigated. The boundary condition is given only on the boundary that is identical to the second half-plane. Note that this condition has a special form. So, the Karleman condition is met for two points moving at the same time on this boundary. The examination of the solution of the considered boundary issue is based on the properties of the necessary conditions obtained in the case. The singularities in the necessary conditions are regularized by means of the given boundary condition.