The higher order regularity Dirichlet problem for elliptic systems in   the upper-half space
  We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in $L^p$-based Sobolev spaces, $1<p<\infty$, of arbitrary smoothness $\ell$, is well-posed in the class of functions whose nontangential maximal operator of their derivatives up to, and including, order $\ell$ is $L^p$-integrable. This class includes all scalar, complex coefficient elliptic operators of second order, as well as the Lam\'e system of elasticity, among others. 
Jos\'e Mar\'ia Martell, Dorina Mitrea, Irina Mitrea and Marius Mitrea
math.AP math.CA