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 norm of the solution in an $varepsilon$-neighbourhood of the boundary can be estimated independently of $varepsilon$.