  Using analysis for 2-admissible functions in weighted Sobolev spaces and
stochastic calculus for possibly degenerate symmetric elliptic forms, we
construct weak solutions to a wide class of stochastic differential equations
starting from an explicitly specified subset in Euclidean space. The solutions
have typically unbounded and discontinuous drift but may still in some cases
start from all points of $\mathbb{R}^d$ and thus in particular from those where
the drift terms are infinite. As a consequence of our approach we are able to
provide new non-explosion criteria for the unique strong solutions of
\cite{Zh}.
