Dirichlet Problem for Poisson Equation on the Rectangle in Infinite Dimensional Hilbert Space-Reference-Cited by-同舟云学术

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

Published:2020-06-30 Issue:2 Volume:5 Page:329-344
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Busovikov V.M.¹²³⁴,Sakbaev V.Zh.¹²³⁴

Affiliation:

1. Moscow Institute of Physics and Technology , Instiutskii per. 9, Dolgoprudny, Moscow region , Russia

2. Institute of Mathematics with Computer Center of the Ufa Science Center of the Russian Academy of Sciences , Chernyshevskii st. 112, Ufa , Russia

3. Institute of Information Technology , Mathematics and Mechanics of the Nizhniy Novgorod State University , Gagarin ave 23, Nizhniy Novgorod , Russia

4. Steklov Mathematical Institute of Russian Academy of Sciences , Gubkin srt.8 , Moscow , Russia

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/amns.2020.2.00016

Reference17 articles.

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2. V.M. Busovikov. Properties of one finite additive measure on lp invariant to shifts. Proceedings of MIPT. 10 (2018) no. 2. 163–172.

3. V.M. Busovikov, V.Zh. Sakbaev. Sobolev spaces of functions on Hilbert space with shift-invariant measure and approximation of semigroups. Izvestiya RAN. Ser. Mathematics. (2020) no. 4.

4. Ya. A. Butko. Chernoff approximation of subordinate semigroups. Stoch. Dyn. 1850021 (2017), 19 p., DOI: 10.1142/S0219493718500211.

5. N. Dunford, J. Schwartz. Linear operators. General Theory. Moscow, 2004.

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