Geodesic
Behaviour near the boundary for solutions of elasticity systems
Electronic journal of differential equations, Tome 1997 (1997)
In this article we study the behaviour near the boundary for weak solutions of the system

$ u''-\mu\Delta u-(\lambda +\mu )\nabla (\alpha (x)\,{\rm div}\, u)=h\,, $

with $u(x,t)=0$ on the boundary of a domain $\Omega\in {\bf R}^n$, 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 $\varepsilon$.
Classification : 93B05, 93C20, 35B37
Keywords: behaviour near the boundary, controllability 
@article{EJDE_1997__1997__a45,
     author = {Domingos Cavalcanti,  Val\'eria Neves},
     title = {Behaviour near the boundary for solutions of elasticity systems},
     journal = {Electronic journal of differential equations},
     year = {1997},
     volume = {1997},
     zbl = {0936.93013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a45/}
}
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VL  - 1997
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%A Domingos Cavalcanti,  Valéria Neves
%T Behaviour near the boundary for solutions of elasticity systems
%J Electronic journal of differential equations
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Domingos Cavalcanti,  Valéria Neves. Behaviour near the boundary for solutions of elasticity systems. Electronic journal of differential equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a45/