Applications of Estimates near the Boundary to Regularity of Solutions in Linearized Elasticity

In this paper the tame estimate of Moser [17] is used to extend the standard regularity estimate of Agmon, Douglis, and Nirenberg [4] for systems of strongly elliptic equations in linearized elasticity so that the components of the elasticity tensor need only lie in the Sobolev space W(Ω) for p > n/m, rather than p > n, when one obtains W–regularity of the solution. This improvement is necessary if one wants to prove global continuation results in such spaces for the equations of nonlinear elasticity.