On a generalization of the Dirichlet problem for the Poisson equation

In this paper, we investigate a generalization of the Dirichlet problem for the Poisson equation in a rectangular domain. We assume that the kth-order normal derivatives of an unknown function are given on lower and upper bases of the rectangle and that homogeneous boundary conditions of the first kind are given on the lateral sides. Under these conditions, we prove the existence of a unique regular solution of this problem.

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