Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 12, pp 1-18.
Title: Behaviour near the boundary for solutions of elasticity systems
Author: V. N. Domingos Cavalcanti (Univ. Estadual de Maringa)
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