  We revisit work of Rost, Dupire and Cox--Wang on connections between Root's
solution of the Skorokhod embedding problem and obstacle problems. We develop
an approach based on viscosity sub- and supersolutions and an accompanying
comparison principle. This gives a complete characterization of (reversed) Root
barriers and leads to new proofs of existence as well as minimality of such
barrier solutions by pure PDE methods. The approach is self-contained and
general enough to cover martingale diffusions with degenerate elliptic or
time-dependent volatility; it also provides insights about the dynamics of
general Skorokhod embeddings.
