On the linearized system of elasticity in the half-space
The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022821?viewType=HTML |
| _version_ | 1828723219549388800 |
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| author | Nabil Kerdid |
| author_facet | Nabil Kerdid |
| author_sort | Nabil Kerdid |
| collection | DOAJ |
| description | The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity. |
| first_indexed | 2024-04-12T12:47:05Z |
| format | Article |
| id | doaj.art-4c11e769e77a4c9f8c5eea31f3706000 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T12:47:05Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-4c11e769e77a4c9f8c5eea31f37060002022-12-22T03:32:36ZengAIMS PressAIMS Mathematics2473-69882022-06-0178149911500110.3934/math.2022821On the linearized system of elasticity in the half-spaceNabil Kerdid 0Department of Mathematics and Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), PO-Box 90950, Riyadh 11623, KSAThe purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity.https://www.aimspress.com/article/doi/10.3934/math.2022821?viewType=HTMLlinear elasticityunbounded domainskorn's inequalityhalf-spaceweighted spaces |
| spellingShingle | Nabil Kerdid On the linearized system of elasticity in the half-space AIMS Mathematics linear elasticity unbounded domains korn's inequality half-space weighted spaces |
| title | On the linearized system of elasticity in the half-space |
| title_full | On the linearized system of elasticity in the half-space |
| title_fullStr | On the linearized system of elasticity in the half-space |
| title_full_unstemmed | On the linearized system of elasticity in the half-space |
| title_short | On the linearized system of elasticity in the half-space |
| title_sort | on the linearized system of elasticity in the half space |
| topic | linear elasticity unbounded domains korn's inequality half-space weighted spaces |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022821?viewType=HTML |
| work_keys_str_mv | AT nabilkerdid onthelinearizedsystemofelasticityinthehalfspace |