Dirichlet Problem for Poisson Equation on the Rectangle in Infinite Dimensional Hilbert Space

Applied Mathematics and Nonlinear Sciences

Busovikov V.M.¹  Sakbaev V.Zh.¹ 

[1] Moscow Institute of Physics and Technology,Instiutskii per. 9, Dolgoprudny, Moscow region, 141701Russia;

关键词: shift invariant measure on banach space;    random walks;    laplas operator;    sobolev space;    dirichlet problem;    35q40;    47n50;    47f05;   

DOI  :  10.2478/amns.2020.2.00016

来源: DOAJ

【 摘 要 】

We study the class of finite additive shift invariant measures on the real separable Hilbert space E. For any choice of such a measure we consider the Hilbert space ℋ of complex-valued functions which are square-integrable with respect to this measure. Some analogs of Sobolev spaces of functions on the space E are introduced. The analogue of Gauss theorem is obtained for the simplest domains such as the rectangle in the space E. The correctness of the problem for Poisson equation in the rectangle with homogeneous Dirichlet condition is obtained and the variational approach of the solving of this problem is constructed.

【 授权许可】

Unknown