On a generalization of the Dirichlet problem for the Poisson equation
Djumaklych AmanovInstitute of Mathematics, National University of Uzbekistan, Durmon yuli 29, Tashkent, 100125, Uzbekistan
ABI
Abstract
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.