Integral representation of the solution of a Gellerstedt problem

The solution of the Gellerstedt problem for the Lavrent’ev-Bitsadze equation was earlier obtained in the form of a series for the case of a half-strip in the elliptic part of the domain and of nonzero boundary data on the characteristics in the hyperbolic part of the domain. In the present paper, we give an integral representation of the solutions of this problem as well as some related problems.