  We deal with general quasilinear divergence-form coercive operators whose
prototype is the $m$-Laplacean operator. The nonlinear terms are given by
Carath\'eodory functions and satisfy controlled growth structure conditions
with data belonging to suitable Morrey spaces. The fairly non-regular boundary
of the underlying domain is supposed to satisfy a capacity density condition
which allows domains with exterior corkscrew property.
  We prove global boundedness and Hoelder continuity up to the boundary for the
weak solutions of such equations, generalizing this way the classical
$L^p$-result of Ladyzhenskaya and Ural'tseva to the settings of the Morrey
spaces.
