Continuation of the solution of the inhomogeneous polyanalytic equation

We consider the ill-posed problem of continuing the solution of an inhomogeneous n – an analytical equation into a domain based on the values of its successive derivatives up to (n −1)-th order on part of the border. An estimate of the conditional stability of the solution to the continuation problem is obtained in the form of an analogue of the theorem on two constants from the theory of functions of a complex variable. An analogue of Carleman’s formula and an existence theorem for a solution to the continuation problem are proved.