Mixed Boundary Value Problems for the Elasticity System in Exterior Domains
We study the properties of solutions of the mixed Dirichlet−Robin and Neumann−Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy int...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/24/2/58 |
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| author | Hovik A. Matevossian |
| author_facet | Hovik A. Matevossian |
| author_sort | Hovik A. Matevossian |
| collection | DOAJ |
| description | We study the properties of solutions of the mixed Dirichlet−Robin and Neumann−Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mi>a</mi> </msup> </semantics> </math> </inline-formula> is finite for such solutions. We use the variational principle and depending on the value of the parameter <i>a</i>, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions. |
| first_indexed | 2024-12-11T00:58:42Z |
| format | Article |
| id | doaj.art-3a1ff5250f6a4ca480ca8e27470f3095 |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-11T00:58:42Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-3a1ff5250f6a4ca480ca8e27470f30952022-12-22T01:26:24ZengMDPI AGMathematical and Computational Applications2297-87472019-06-012425810.3390/mca24020058mca24020058Mixed Boundary Value Problems for the Elasticity System in Exterior DomainsHovik A. Matevossian0Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov str., 40, Moscow 119333, RussiaWe study the properties of solutions of the mixed Dirichlet−Robin and Neumann−Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mi>a</mi> </msup> </semantics> </math> </inline-formula> is finite for such solutions. We use the variational principle and depending on the value of the parameter <i>a</i>, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.https://www.mdpi.com/2297-8747/24/2/58elasticity systemDirichlet–Robin problemNeumann–Robin problemSobolev spaceweighted energy integral |
| spellingShingle | Hovik A. Matevossian Mixed Boundary Value Problems for the Elasticity System in Exterior Domains Mathematical and Computational Applications elasticity system Dirichlet–Robin problem Neumann–Robin problem Sobolev space weighted energy integral |
| title | Mixed Boundary Value Problems for the Elasticity System in Exterior Domains |
| title_full | Mixed Boundary Value Problems for the Elasticity System in Exterior Domains |
| title_fullStr | Mixed Boundary Value Problems for the Elasticity System in Exterior Domains |
| title_full_unstemmed | Mixed Boundary Value Problems for the Elasticity System in Exterior Domains |
| title_short | Mixed Boundary Value Problems for the Elasticity System in Exterior Domains |
| title_sort | mixed boundary value problems for the elasticity system in exterior domains |
| topic | elasticity system Dirichlet–Robin problem Neumann–Robin problem Sobolev space weighted energy integral |
| url | https://www.mdpi.com/2297-8747/24/2/58 |
| work_keys_str_mv | AT hovikamatevossian mixedboundaryvalueproblemsfortheelasticitysysteminexteriordomains |