  This paper deals with solutions of the divergence for domains with external
cusps. It is known that the classic results in standard Sobolev spaces, which
are basic in the variational analysis of the Stokes equations, are not valid
for this class of domains.
  For some bounded domains $\Omega\subset{\mathbb R}^n$ presenting power type
cusps of integer dimension $m\le n-2$, we prove the existence of solutions of
the equation ${div}{\bf u}=f$ in weighted Sobolev spaces, where the weights are
powers of the distance to the cusp. The results obtained are optimal in the
sense that the powers cannot be improved.
  As an application, we prove existence and uniqueness of solutions of the
Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain
weighted Korn type inequalities for this class of domains.
