Biharmonic Problem with Steklov-type Conditions on the Boundary of the Domain

This paper considers a biharmonic problem with a Steklov-type boundary condition on the boundary. For this problem, questions of both uniqueness and non-uniqueness of solutions are studied under the condition that the weighted Dirichlet integral is bounded, and for which the exact number of linear i...

Full description

Saved in:
Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 12; pp. 6552 - 6568
Main Author Matevossian, H. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Boundary conditions
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Solution space
Uniqueness
2010 Mathematics Subject Classification: 35G15, 35J35, 35J40, 35J57
Dirichlet integral
Steklov-type boundary conditions
biharmonic equation
weighted Sobolev spaces
Online AccessGet full text

Cover

More Information
Summary:This paper considers a biharmonic problem with a Steklov-type boundary condition on the boundary. For this problem, questions of both uniqueness and non-uniqueness of solutions are studied under the condition that the weighted Dirichlet integral is bounded, and for which the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the solution space depending on the value of the parameter included in the weighted Dirichlet integral.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224607677