The solution of the mixed boundary value problem of Dirichlet- Neumann for the Poisson equation in a multidimensional infinite layer

Authors: Algazin O.D., Kopaev A.V. Published: 15.06.2016
Published in issue: #3(66)/2016  
DOI: 10.18698/1812-3368-2016-3-42-56

Category: Mathematics and Mechanics | Chapter: Mathematical Physics  
Keywords: Fourier transform, Poisson equation, mixed boundary value problem, tempered distributions, Green’s function

In this research by the method of Fourier transform we solve the mixed boundary value problem of Dirichlet - Neumann for the Poisson equation in the domain bounded by two parallel hyperplanes in Rn. The solution is represented as a sum of integrals whose kernels are found in the final form. In particular, we constructed Green’s function of the Laplace operator for the mixed boundary value problem of Dirichlet - Neumann, by which the solution of the problem is written. If the given boundary values are tempered distributions, the solution of the mixed boundary value problem for the homogeneous equation (Laplace) is written as the convolution of the kernels with these distributions.


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