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...

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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
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Abstract 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.
AbstractList 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.
Author Matevossian, H. A.
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Cites_doi 10.24033/asens.510
10.1134/S1061920818020115
10.1007/978-3-642-96379-7
10.1002/mana.200310344
10.1002/1521-4001(200101)81:1<69::AID-ZAMM69>3.0.CO;2-#
10.1023/A:1012347929056
10.1070/RM1988v043n05ABEH001945
10.1134/S1995080221080205
10.1137/0501032
10.1007/BF00251392
10.1007/978-3-642-12245-3
10.1070/SM2001v192n12ABEH000615
10.1016/0022-247X(68)90123-6
10.1134/S1061920817010125
10.1134/S0081543806040031
10.1080/02781070500087394
10.1070/IM2003v067n05ABEH000451
10.1134/S1995080224604399
10.1134/S0001434615110358
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Issue 12
Keywords 2010 Mathematics Subject Classification: 35G15, 35J35, 35J40, 35J57
Dirichlet integral
Steklov-type boundary conditions
biharmonic equation
weighted Sobolev spaces
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References S. G. Mikhlin (8122_CR24) 1977
H. A. Matevossian (8122_CR23) 2024; 45
H. Begehr (8122_CR1) 2005; 13
F. Cakoni (8122_CR5) 2005; 50
L. E. Payne (8122_CR25) 1970; 1
H. A. Matevossian (8122_CR18) 2018; 25
K. Rektorys (8122_CR26) 1980
8122_CR27
8122_CR28
H. A. Matevossian (8122_CR19) 2019; 64
H. Begehr (8122_CR2) 2006; 255
O. A. Matevosyan (8122_CR13) 2001; 70
V. A. Kondratiev (8122_CR11) 1990; 10
S. F. Chichoyan (8122_CR6) 2015; 98
H. A. Matevossian (8122_CR15) 2003; 67
F. Brock (8122_CR4) 2001; 81
O. A. Matevossian (8122_CR14) 2001; 192
H. A. Matevossian (8122_CR16) 2017; 9
H. Begehr (8122_CR3) 2006; 279
cr-split#-8122_CR29.2
cr-split#-8122_CR29.1
V. A. Kondrat’ev (8122_CR10) 1988; 43
H. A. Matevossian (8122_CR20) 2020; 8
8122_CR7
J. R. Kuttler (8122_CR12) 1968; 23
H. A. Matevossian (8122_CR22) 2023; 30
D. Gilbarg (8122_CR8) 1977
G. Migliaccio (8122_CR21) 2021; 42
H. A. Matevossian (8122_CR17) 2017; 24
V. A. Kondratiev (8122_CR9) 1987; 99
References_xml – ident: #cr-split#-8122_CR29.1
  doi: 10.24033/asens.510
– volume: 10
  start-page: 641
  year: 1990
  ident: 8122_CR11
  publication-title: Ser. VII
– volume: 25
  start-page: 271
  year: 2018
  ident: 8122_CR18
  publication-title: Russ. J. Math. Phys.
  doi: 10.1134/S1061920818020115
– volume-title: Elliptic Partial Differential Equations of Second Order
  year: 1977
  ident: 8122_CR8
  doi: 10.1007/978-3-642-96379-7
– volume: 279
  start-page: 38
  year: 2006
  ident: 8122_CR3
  publication-title: Math. Nachr.
  doi: 10.1002/mana.200310344
– ident: 8122_CR27
– volume: 13
  start-page: 65
  year: 2005
  ident: 8122_CR1
  publication-title: Gen. Math.
– volume: 81
  start-page: 69
  year: 2001
  ident: 8122_CR4
  publication-title: Z. Angew. Math. Mech.
  doi: 10.1002/1521-4001(200101)81:1<69::AID-ZAMM69>3.0.CO;2-#
– volume: 70
  start-page: 363
  year: 2001
  ident: 8122_CR13
  publication-title: Math. Notes
  doi: 10.1023/A:1012347929056
– volume: 43
  start-page: 65
  year: 1988
  ident: 8122_CR10
  publication-title: Russ. Math. Surv.
  doi: 10.1070/RM1988v043n05ABEH001945
– volume: 42
  start-page: 1886
  year: 2021
  ident: 8122_CR21
  publication-title: Lobachevskii J. Math.
  doi: 10.1134/S1995080221080205
– volume: 1
  start-page: 354
  year: 1970
  ident: 8122_CR25
  publication-title: SIAM J. Math. Anal.
  doi: 10.1137/0501032
– volume: 99
  start-page: 75
  year: 1987
  ident: 8122_CR9
  publication-title: Arch. Ration. Mech. Anal.
  doi: 10.1007/BF00251392
– ident: 8122_CR7
  doi: 10.1007/978-3-642-12245-3
– volume: 192
  start-page: 1763
  year: 2001
  ident: 8122_CR14
  publication-title: Sb. Math.
  doi: 10.1070/SM2001v192n12ABEH000615
– volume: 23
  start-page: 148
  year: 1968
  ident: 8122_CR12
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(68)90123-6
– volume: 64
  start-page: 1
  year: 2019
  ident: 8122_CR19
  publication-title: Equat.
– volume: 24
  start-page: 134
  year: 2017
  ident: 8122_CR17
  publication-title: Russ. J. Math. Phys.
  doi: 10.1134/S1061920817010125
– volume: 255
  start-page: 13
  year: 2006
  ident: 8122_CR2
  publication-title: Proc. Steklov Math. Inst.
  doi: 10.1134/S0081543806040031
– volume-title: Linear Partial Differential Equations
  year: 1977
  ident: 8122_CR24
– volume-title: Variational Methods in Mathematics, Science and Engineering
  year: 1980
  ident: 8122_CR26
– volume: 50
  start-page: 681
  year: 2005
  ident: 8122_CR5
  publication-title: Complex Variab.
  doi: 10.1080/02781070500087394
– volume: 8
  start-page: 2241
  year: 2020
  ident: 8122_CR20
  publication-title: MDPI Math.
– volume: 67
  start-page: 895
  year: 2003
  ident: 8122_CR15
  publication-title: Izv. Math.
  doi: 10.1070/IM2003v067n05ABEH000451
– ident: 8122_CR28
  doi: 10.24033/asens.510
– volume: 9
  start-page: 151
  year: 2017
  ident: 8122_CR16
  publication-title: Anal. Appl.
– volume: 45
  start-page: 3629
  year: 2024
  ident: 8122_CR23
  publication-title: Lobachevskii J. Math.
  doi: 10.1134/S1995080224604399
– volume: 98
  start-page: 999
  year: 2015
  ident: 8122_CR6
  publication-title: Math. Notes
  doi: 10.1134/S0001434615110358
– volume: 30
  start-page: 713
  year: 2023
  ident: 8122_CR22
  publication-title: Russ. J. Math. Phys.
  doi: 10.1134/S1061920823040209
– ident: #cr-split#-8122_CR29.2
  doi: 10.24033/asens.516
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Snippet This paper considers a biharmonic problem with a Steklov-type boundary condition on the boundary. For this problem, questions of both uniqueness and...
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StartPage 6552
SubjectTerms Algebra
Analysis
Boundary conditions
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Solution space
Uniqueness
Title Biharmonic Problem with Steklov-type Conditions on the Boundary of the Domain
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