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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 6, Pages 951–965
DOI: https://doi.org/10.31857/S0044466921060089 (Mi zvmmf11251) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Partial Differential Equations

Biharmonic problem with Dirichlet and Steklov-type boundary conditions in weighted spaces

H. A. Matevossianab

a Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Aviation Institute (National Research University "MAI"), 125993, Moscow, Russia
Citations (2)
DOI: https://doi.org/10.31857/S0044466921060089
Abstract: The uniqueness of solutions of a biharmonic problem with Dirichlet and Steklov-type boundary conditions in the exterior of a compact set are studied under the assumption that the generalized solution of this problem has a finite Dirichlet integral with a weight $|x|^a$. Depending on the parameter $a$, uniqueness (non-uniqueness) theorems are proved and exact formulas for calculating the dimension of the solution space of this biharmonic problem are found.
Key words: biharmonic operator, Dirichlet and Steklov-type boundary conditions, weighted Dirichlet integral, Sobolev spaces.
Received: 29.07.2020
Revised: 16.11.2020
Accepted: 11.02.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 6, Pages 938–952
DOI: https://doi.org/10.1134/S0965542521060087
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: H. A. Matevossian, “Biharmonic problem with Dirichlet and Steklov-type boundary conditions in weighted spaces”, Zh. Vychisl. Mat. Mat. Fiz., 61:6 (2021), 951–965; Comput. Math. Math. Phys., 61:6 (2021), 938–952
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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