Behaviour near the boundary for solutions of elasticity systems
In this article we study the behaviour near the boundary for weak solutions of the system $$ u''-muDelta u-(lambda +mu )abla (alpha (x),{ m div}, u)=h,, $$ with $u(x,t)=0$ on the boundary of a domain $Omegain {R}^n$, and $u(x,0)=u^0$, $u'(x,0)=u^1$ in $Omega$. We show that the Sobolev...
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| Format: | Article |
| Language: | English |
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Texas State University
1997-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1997/12/abstr.html |
| _version_ | 1819123497248489472 |
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| author | Valeria N. Domingos Cavalcanti |
| author_facet | Valeria N. Domingos Cavalcanti |
| author_sort | Valeria N. Domingos Cavalcanti |
| collection | DOAJ |
| description | In this article we study the behaviour near the boundary for weak solutions of the system $$ u''-muDelta u-(lambda +mu )abla (alpha (x),{ m div}, u)=h,, $$ with $u(x,t)=0$ on the boundary of a domain $Omegain {R}^n$, and $u(x,0)=u^0$, $u'(x,0)=u^1$ in $Omega$. We show that the Sobolev norm of the solution in an $varepsilon$-neighbourhood of the boundary can be estimated independently of $varepsilon$. |
| first_indexed | 2024-12-22T07:09:17Z |
| format | Article |
| id | doaj.art-e83bccc33d374e6cb134c82f6291b57f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T07:09:17Z |
| publishDate | 1997-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e83bccc33d374e6cb134c82f6291b57f2022-12-21T18:34:34ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911997-07-01199712118Behaviour near the boundary for solutions of elasticity systemsValeria N. Domingos CavalcantiIn this article we study the behaviour near the boundary for weak solutions of the system $$ u''-muDelta u-(lambda +mu )abla (alpha (x),{ m div}, u)=h,, $$ with $u(x,t)=0$ on the boundary of a domain $Omegain {R}^n$, and $u(x,0)=u^0$, $u'(x,0)=u^1$ in $Omega$. We show that the Sobolev norm of the solution in an $varepsilon$-neighbourhood of the boundary can be estimated independently of $varepsilon$.http://ejde.math.txstate.edu/Volumes/1997/12/abstr.htmlBehaviour near the boundarycontrollabilityelasticity system |
| spellingShingle | Valeria N. Domingos Cavalcanti Behaviour near the boundary for solutions of elasticity systems Electronic Journal of Differential Equations Behaviour near the boundary controllability elasticity system |
| title | Behaviour near the boundary for solutions of elasticity systems |
| title_full | Behaviour near the boundary for solutions of elasticity systems |
| title_fullStr | Behaviour near the boundary for solutions of elasticity systems |
| title_full_unstemmed | Behaviour near the boundary for solutions of elasticity systems |
| title_short | Behaviour near the boundary for solutions of elasticity systems |
| title_sort | behaviour near the boundary for solutions of elasticity systems |
| topic | Behaviour near the boundary controllability elasticity system |
| url | http://ejde.math.txstate.edu/Volumes/1997/12/abstr.html |
| work_keys_str_mv | AT valeriandomingoscavalcanti behaviourneartheboundaryforsolutionsofelasticitysystems |