Electron. J. Diff. Eqns., Vol. 1997(1997), No. 12, pp 1-18.

Behaviour near the boundary for solutions of elasticity systems

V. N. Domingos Cavalcanti

Abstract:
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 $\varepsilon$.

Submitted April 1, 1997. Published July 31, 1997.
Math Subject Classification: 93B05, 93C20, 35B37.
Key Words: Behaviour near the boundary, controllability, elasticity system

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Valeria N. Domingos Cavalcanti
Universidade Estadual de Maringa,
87020-900 Maringa-PR, Brazil
e-mail: valeria@gauss.dma.uem.br

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