  We study global regularity for solutions of quasilinear elliptic equations of
the form $\div \A(x,u,\nabla u) = \div \F $ in rough domains $\Omega$ in $\R^n$
with nonhomogeneous Dirichlet boundary condition. The vector field $\A$ is
assumed to be continuous in $u$, and its growth in $\nabla u$ is like that of
the $p$-Laplace operator. We establish global gradient estimates in weighted
Morrey spaces for weak solutions $u$ to the equation under the Reifenberg flat
condition for $\Omega$, a small BMO condition in $x$ for $\A$, and an optimal
condition for the Dirichlet boundary data.
