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 |
| Summary: | 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. |
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| ISSN: | 2297-8747 |