  We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ of a
Beltrami equation $\overline{\partial}f=\mu\,\partial f$ in a domain
$D\subseteq\Bbb C$ is the so--called ring $Q-$homeomorphism with
$Q(z)=K^T_{\mu}(z, z_0)$ where $K^T_{\mu}(z, z_0)$ is the tangent (angular)
dilatation quotient of the equation with respect to an arbitrary point $z_0\in
{\overline{D}}$. In this connection, we develop the theory of the boundary
behavior of the ring $Q-$homeomorphisms with respect to prime ends. On this
basis, we show that, for wide classes of degenerate Beltrami equations
$\overline{\partial}f=\mu\,\partial f$, there exist regular solutions of the
Dirichlet problem in arbitrary simply connected domains in $\Bbb C$ and
pseudoregular and multivalent solutions in arbitrary finitely connected domains
in $\Bbb C$ with boundary datum $\varphi$ that are continuous with respect to
the topology of prime ends.
