I want to prove the following statement:
Let $\Omega$ be bounded, polygonal, and convex, then for the solution of the linear elasticity (elliptic) equation with inhomogenous Dirichlet boundary data $g\in W^{2-\frac{1}{p}}_p(\partial \Omega)$: \begin{align} Lu &= 0, \text{ in } \Omega \\[3pt] u &= g, \text{ on } \partial \Omega \end{align} it holds that \begin{equation}\|u\|_{W^{2}_p(\Omega)} \leq c \|g\|_{W^{2-\frac{1}{p}}_p(\partial\Omega)}.\end{equation}
I have found a result by Grisvard stating that a (unique) solution exists in $W^2_p$, but there is no stability estimate provided.
On the other hand there are results for the homogenous Dirichlet case (e.g. also by Grisvard) with a righthand side in $L^2(\Omega)$. So all I am missing is a continuous extension operator from $W^{2-\frac{1}{p}}_p(\partial \Omega)$ to $W^2_p(\Omega)$. Unfortunately I have so far only found the reverse, i.e. the existance of a continuous trace operator.
Can somebody point out a reference where either the original statement is shown or the continuity of such an extension operator is shown? Thanks a lot!