On a generalization of the Dirichlet problem for the Poisson equation

Boundary value problems

Djumaklych Amanov¹ 

[1] Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

关键词: Poisson equation;    Dirichlet problem;    regular solution;    uniqueness of a solution;    existence of a solution;    35J25;   

DOI  :  10.1186/s13661-016-0668-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY