Behaviour Near the Boundary for Solutions of Elasticity Systems
Domingos Cavalcanti, V. N.
Southwest Texas State University, Department of Mathematics
<p>In this article we study the behaviour near the boundary for weak solutions of the system</p> <pre>u'' − µ∆u − (λ + µ)∇(α(x) div u) = h,</pre> <p>with u(x, t) = 0 on the boundary of a domain Ω ∈ <b>R</b><sup>n</sup>, and u(x, 0) = u<sup>0</sup>, u' (x, 0) = u<sup>1</sup> in Ω. We show that the Sobolev norm of the solution in an ε-neighbourhood of the boundary can be estimated independently of ε.</p>
Behaviour near the boundary, Controllability, Elasticity system
Domingos Cavalcanti, V. N. (1997). Behaviour near the boundary for solutions of elasticity systems. <i>Electronic Journal of Differential Equations, 1997</i>(12), pp. 1-18.